diff --git a/include/ceres/internal/householder_vector.h b/include/ceres/internal/householder_vector.h
index 55f68e5..e5fc9bf 100644
--- a/include/ceres/internal/householder_vector.h
+++ b/include/ceres/internal/householder_vector.h
@@ -82,6 +82,14 @@
   v->head(v->rows() - 1) /= v_pivot;
 }
 
+template <typename XVectorType, typename Scalar, int N>
+Eigen::Matrix<Scalar, N, 1> ApplyHouseholderVector(
+    const XVectorType& y,
+    const Eigen::Matrix<Scalar, N, 1>& v,
+    const Scalar& beta) {
+  return (y - v * (beta * (v.transpose() * y)));
+}
+
 }  // namespace internal
 }  // namespace ceres
 
diff --git a/include/ceres/internal/sphere_manifold.h b/include/ceres/internal/sphere_manifold.h
new file mode 100644
index 0000000..c29fbcc
--- /dev/null
+++ b/include/ceres/internal/sphere_manifold.h
@@ -0,0 +1,186 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2022 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+//   this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+//   used to endorse or promote products derived from this software without
+//   specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: vitus@google.com (Mike Vitus)
+//         jodebo_beck@gmx.de (Johannes Beck)
+
+#include "ceres/internal/householder_vector.h"
+
+namespace ceres {
+
+template <int AmbientSpaceDimension>
+SphereManifold<AmbientSpaceDimension>::SphereManifold()
+    : size_{AmbientSpaceDimension} {
+  static_assert(
+      AmbientSpaceDimension != Eigen::Dynamic,
+      "The size is set to dynamic. Please call the constructor with a size.");
+}
+
+template <int AmbientSpaceDimension>
+SphereManifold<AmbientSpaceDimension>::SphereManifold(int size) : size_{size} {
+  if (AmbientSpaceDimension != Eigen::Dynamic) {
+    CHECK_EQ(AmbientSpaceDimension, size)
+        << "Specified size by template parameter differs from the supplied "
+           "one.";
+  } else {
+    CHECK_GT(size_, 1)
+        << "The size of the manifold needs to be greater than 1.";
+  }
+}
+
+template <int AmbientSpaceDimension>
+bool SphereManifold<AmbientSpaceDimension>::Plus(
+    const double* x_ptr,
+    const double* delta_ptr,
+    double* x_plus_delta_ptr) const {
+  Eigen::Map<const AmbientVector> x(x_ptr, size_);
+  Eigen::Map<const TangentVector> delta(delta_ptr, size_ - 1);
+  Eigen::Map<AmbientVector> x_plus_delta(x_plus_delta_ptr, size_);
+
+  const double norm_delta = delta.norm();
+
+  if (norm_delta == 0.0) {
+    x_plus_delta = x;
+    return true;
+  }
+
+  // Map the delta from the minimum representation to the over parameterized
+  // homogeneous vector. See B.2 p.25 equation (106) - (107) for more details.
+  const double norm_delta_div_2 = 0.5 * norm_delta;
+  const double sin_delta_by_delta =
+      std::sin(norm_delta_div_2) / norm_delta_div_2;
+
+  AmbientVector y(size_);
+  y.head(size_ - 1) = 0.5 * sin_delta_by_delta * delta;
+  y(size_ - 1) = std::cos(norm_delta_div_2);
+
+  AmbientVector v(size_);
+  double beta;
+
+  // NOTE: The explicit template arguments are needed here because
+  // ComputeHouseholderVector is templated and some versions of MSVC
+  // have trouble deducing the type of v automatically.
+  internal::ComputeHouseholderVector<Eigen::Map<const AmbientVector>,
+                                     double,
+                                     AmbientSpaceDimension>(x, &v, &beta);
+
+  // Apply the delta update to remain on the sphere.
+  x_plus_delta = x.norm() * internal::ApplyHouseholderVector(y, v, beta);
+
+  return true;
+}
+
+template <int AmbientSpaceDimension>
+bool SphereManifold<AmbientSpaceDimension>::PlusJacobian(
+    const double* x_ptr, double* jacobian_ptr) const {
+  Eigen::Map<const AmbientVector> x(x_ptr, size_);
+  Eigen::Map<MatrixPlusJacobian> jacobian(jacobian_ptr, size_, size_ - 1);
+
+  AmbientVector v(size_);
+  double beta;
+
+  // NOTE: The explicit template arguments are needed here because
+  // ComputeHouseholderVector is templated and some versions of MSVC
+  // have trouble deducing the type of v automatically.
+  internal::ComputeHouseholderVector<Eigen::Map<const AmbientVector>,
+                                     double,
+                                     AmbientSpaceDimension>(x, &v, &beta);
+
+  // The Jacobian is equal to J = 0.5 * H.leftCols(size_ - 1) where H is the
+  // Householder matrix (H = I - beta * v * v').
+  for (int i = 0; i < size_ - 1; ++i) {
+    jacobian.col(i) = -0.5 * beta * v(i) * v;
+    jacobian.col(i)(i) += 0.5;
+  }
+  jacobian *= x.norm();
+
+  return true;
+}
+
+template <int AmbientSpaceDimension>
+bool SphereManifold<AmbientSpaceDimension>::Minus(const double* y_ptr,
+                                                  const double* x_ptr,
+                                                  double* y_minus_x_ptr) const {
+  AmbientVector y = Eigen::Map<const AmbientVector>(y_ptr, size_);
+  Eigen::Map<const AmbientVector> x(x_ptr, size_);
+  Eigen::Map<TangentVector> y_minus_x(y_minus_x_ptr, size_ - 1);
+
+  // Apply hoseholder transformation.
+  AmbientVector v(size_);
+  double beta;
+
+  // NOTE: The explicit template arguments are needed here because
+  // ComputeHouseholderVector is templated and some versions of MSVC
+  // have trouble deducing the type of v automatically.
+  internal::ComputeHouseholderVector<Eigen::Map<const AmbientVector>,
+                                     double,
+                                     AmbientSpaceDimension>(x, &v, &beta);
+
+  const AmbientVector hy =
+      internal::ApplyHouseholderVector(y, v, beta) / x.norm();
+
+  // Calculate y - x. See B.2 p.25 equation (108).
+  double y_last = hy[size_ - 1];
+  double hy_norm = hy.head(size_ - 1).norm();
+  if (hy_norm == 0.0) {
+    y_minus_x.setZero();
+  } else {
+    y_minus_x =
+        2.0 * std::atan2(hy_norm, y_last) / hy_norm * hy.head(size_ - 1);
+  }
+
+  return true;
+}
+
+template <int AmbientSpaceDimension>
+bool SphereManifold<AmbientSpaceDimension>::MinusJacobian(
+    const double* x_ptr, double* jacobian_ptr) const {
+  Eigen::Map<const AmbientVector> x(x_ptr, size_);
+  Eigen::Map<MatrixMinusJacobian> jacobian(jacobian_ptr, size_ - 1, size_);
+
+  AmbientVector v(size_);
+  double beta;
+
+  // NOTE: The explicit template arguments are needed here because
+  // ComputeHouseholderVector is templated and some versions of MSVC
+  // have trouble deducing the type of v automatically.
+  internal::ComputeHouseholderVector<Eigen::Map<const AmbientVector>,
+                                     double,
+                                     AmbientSpaceDimension>(x, &v, &beta);
+
+  // The Jacobian is equal to J = 2.0 * H.leftCols(size_ - 1) where H is the
+  // Householder matrix (H = I - beta * v * v').
+  for (int i = 0; i < size_ - 1; ++i) {
+    jacobian.row(i) = -2.0 * beta * v(i) * v;
+    jacobian.row(i)(i) += 2.0;
+  }
+  jacobian /= x.norm();
+
+  return true;
+}
+}  // namespace ceres
\ No newline at end of file
diff --git a/include/ceres/manifold.h b/include/ceres/manifold.h
index 85394b7..ef4b2a7 100644
--- a/include/ceres/manifold.h
+++ b/include/ceres/manifold.h
@@ -31,12 +31,14 @@
 #ifndef CERES_PUBLIC_MANIFOLD_H_
 #define CERES_PUBLIC_MANIFOLD_H_
 
+#include <Eigen/Core>
 #include <array>
 #include <memory>
 #include <vector>
 
 #include "ceres/internal/disable_warnings.h"
 #include "ceres/internal/port.h"
+#include "ceres/types.h"
 
 namespace ceres {
 
@@ -407,8 +409,87 @@
   bool MinusJacobian(const double* x, double* jacobian) const override;
 };
 
+// This provides a manifold on a sphere meaning that the norm of the vector
+// stays the same. Such cases often arises in Structure for Motion
+// problems. One example where they are used is in representing points whose
+// triangulation is ill-conditioned. Here it is advantageous to use an
+// over-parameterization since homogeneous vectors can represent points at
+// infinity.
+//
+// The plus operator is defined as
+//  Plus(x, delta) =
+//    [sin(0.5 * |delta|) * delta / |delta|, cos(0.5 * |delta|)] * x
+//
+// The minus operator is defined as
+//  Minus(x, y) = 2 atan2(nhy, y[-1]) / nhy * hy[0 : size_ - 1]
+// with nhy = norm(hy[0 : size_ - 1])
+//
+// with * defined as an operator which applies the update orthogonal to x to
+// remain on the sphere. The ambient space dimension is required to be greater
+// than 1.
+//
+// The class works with dynamic and static ambient space dimensions. If the
+// ambient space dimensions is know at compile time use
+//    SphereManifold<3> manifold;
+// If the ambient space dimensions is not known at compile time the template
+// parameter needs to be set to ceres::DYNAMIC and the actual dimension needs to
+// be provided as a constructor argument:
+//    SphereManifold<ceres::DYNAMIC> manifold(ambient_dim);
+//
+// See  section B.2 (p.25) in "Integrating Generic Sensor Fusion Algorithms with
+// Sound State Representations through Encapsulation of Manifolds" by C.
+// Hertzberg, R. Wagner, U. Frese and L. Schroder for more details
+// (https://arxiv.org/pdf/1107.1119.pdf)
+template <int AmbientSpaceDimension>
+class SphereManifold : public Manifold {
+ public:
+  static_assert(
+      AmbientSpaceDimension == DYNAMIC || AmbientSpaceDimension > 1,
+      "The size of the homogeneous vector needs to be greater than 1.");
+  static_assert(DYNAMIC == Eigen::Dynamic,
+                "ceres::DYNAMIC needs to be the same as Eigen::Dynamic.");
+
+  SphereManifold();
+  explicit SphereManifold(int size);
+
+  int AmbientSize() const override {
+    return AmbientSpaceDimension == ceres::DYNAMIC ? size_
+                                                   : AmbientSpaceDimension;
+  }
+  int TangentSize() const override { return AmbientSize() - 1; }
+
+  bool Plus(const double* x,
+            const double* delta,
+            double* x_plus_delta) const override;
+  bool PlusJacobian(const double* x, double* jacobian) const override;
+
+  bool Minus(const double* y,
+             const double* x,
+             double* y_minus_x) const override;
+  bool MinusJacobian(const double* x, double* jacobian) const override;
+
+ private:
+  static constexpr int TangentSpaceDimension =
+      AmbientSpaceDimension > 0 ? AmbientSpaceDimension - 1 : Eigen::Dynamic;
+
+  using AmbientVector = Eigen::Matrix<double, AmbientSpaceDimension, 1>;
+  using TangentVector = Eigen::Matrix<double, TangentSpaceDimension, 1>;
+  using MatrixPlusJacobian = Eigen::Matrix<double,
+                                           AmbientSpaceDimension,
+                                           TangentSpaceDimension,
+                                           Eigen::RowMajor>;
+  using MatrixMinusJacobian = Eigen::Matrix<double,
+                                            TangentSpaceDimension,
+                                            AmbientSpaceDimension,
+                                            Eigen::RowMajor>;
+
+  const int size_{};
+};
+
 }  // namespace ceres
 
+#include "internal/sphere_manifold.h"
+
 // clang-format off
 #include "ceres/internal/reenable_warnings.h"
 
diff --git a/internal/ceres/manifold_test.cc b/internal/ceres/manifold_test.cc
index 11d6977..89e0ec7 100644
--- a/internal/ceres/manifold_test.cc
+++ b/internal/ceres/manifold_test.cc
@@ -337,7 +337,7 @@
   return true;
 }
 
-Vector RandomQuaternion() {
+static Vector RandomQuaternion() {
   Vector x = Vector::Random(4);
   x.normalize();
   return x;
@@ -451,5 +451,112 @@
   }
 }
 
+TEST(SphereManifold, ZeroTest) {
+  Eigen::Vector4d x{0.0, 0.0, 0.0, 1.0};
+  Eigen::Vector3d delta = Eigen::Vector3d::Zero();
+  Eigen::Vector4d y = Eigen::Vector4d::Zero();
+
+  SphereManifold<4> manifold;
+  manifold.Plus(x.data(), delta.data(), y.data());
+  EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
+}
+
+TEST(SphereManifold, NearZeroTest1) {
+  Eigen::Vector4d x{1e-5, 1e-5, 1e-5, 1.0};
+  x.normalize();
+  Eigen::Vector3d delta{0.0, 1.0, 0.0};
+  Eigen::Vector4d y = Eigen::Vector4d::Zero();
+
+  SphereManifold<4> manifold;
+  manifold.Plus(x.data(), delta.data(), y.data());
+  EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
+}
+
+TEST(SphereManifold, NearZeroTest2) {
+  Eigen::Vector4d x{0.001, 0.0, 0.0, 0.0};
+  Eigen::Vector3d delta{0.0, 1.0, 0.0};
+  Eigen::Vector4d y = Eigen::Vector4d::Zero();
+  SphereManifold<4> manifold;
+  manifold.Plus(x.data(), delta.data(), y.data());
+  EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
+}
+
+TEST(SphereManifold, Plus) {
+  Eigen::Vector3d x{0.0, 0.0, 1.0};
+  SphereManifold<3> manifold;
+
+  {
+    Eigen::Vector2d delta{M_PI, 0.0};
+    Eigen::Vector3d y = Eigen::Vector3d::Zero();
+    EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
+    const Eigen::Vector3d gtY = Eigen::Vector3d::UnitX();
+    EXPECT_LT((y - gtY).norm(), kTolerance);
+  }
+
+  {
+    Eigen::Vector2d delta{0.0, M_PI};
+    Eigen::Vector3d y = Eigen::Vector3d::Zero();
+    EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
+    const Eigen::Vector3d gtY = Eigen::Vector3d::UnitY();
+    EXPECT_LT((y - gtY).norm(), kTolerance);
+  }
+
+  {
+    Eigen::Vector2d delta = Eigen::Vector2d(1, 1).normalized() * M_PI;
+    Eigen::Vector3d y = Eigen::Vector3d::Zero();
+    EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
+    const Eigen::Vector3d gtY(std::sqrt(2.0) / 2.0, std::sqrt(2.0) / 2.0, 0.0);
+    EXPECT_LT((y - gtY).norm(), kTolerance);
+  }
+}
+
+TEST(SphereManifold, DeathTests) {
+  EXPECT_DEATH_IF_SUPPORTED(SphereManifold<Eigen::Dynamic> x(1), "size");
+}
+
+TEST(SphereManifold, NormalFunctionTest) {
+  SphereManifold<4> manifold;
+  EXPECT_EQ(manifold.AmbientSize(), 4);
+  EXPECT_EQ(manifold.TangentSize(), 3);
+
+  Vector zero_tangent = Vector::Zero(manifold.TangentSize());
+  for (int trial = 0; trial < kNumTrials; ++trial) {
+    const Vector x = Vector::Random(manifold.AmbientSize());
+    Vector y = Vector::Random(manifold.AmbientSize());
+    Vector delta = Vector::Random(manifold.TangentSize());
+
+    if (x.norm() == 0.0 || y.norm() == 0.0) {
+      continue;
+    }
+
+    // X and y need to have the same length.
+    y *= x.norm() / y.norm();
+
+    EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
+  }
+}
+
+TEST(SphereManifold, NormalFunctionTestDynamic) {
+  SphereManifold<Eigen::Dynamic> manifold(5);
+  EXPECT_EQ(manifold.AmbientSize(), 5);
+  EXPECT_EQ(manifold.TangentSize(), 4);
+
+  Vector zero_tangent = Vector::Zero(manifold.TangentSize());
+  for (int trial = 0; trial < kNumTrials; ++trial) {
+    const Vector x = Vector::Random(manifold.AmbientSize());
+    Vector y = Vector::Random(manifold.AmbientSize());
+    Vector delta = Vector::Random(manifold.TangentSize());
+
+    if (x.norm() == 0.0 || y.norm() == 0.0) {
+      continue;
+    }
+
+    // X and y need to have the same length.
+    y *= x.norm() / y.norm();
+
+    EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
+  }
+}
+
 }  // namespace internal
 }  // namespace ceres