diff --git a/include/ceres/gradient_checker.h b/include/ceres/gradient_checker.h
index b79cf86..77f2c8e 100644
--- a/include/ceres/gradient_checker.h
+++ b/include/ceres/gradient_checker.h
@@ -1,5 +1,5 @@
 // Ceres Solver - A fast non-linear least squares minimizer
-// Copyright 2019 Google Inc. All rights reserved.
+// Copyright 2023 Google Inc. All rights reserved.
 // http://ceres-solver.org/
 //
 // Redistribution and use in source and binary forms, with or without
@@ -25,7 +25,7 @@
 // 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.
-// Copyright 2007 Google Inc. All Rights Reserved.
+// Copyright 2023 Google Inc. All Rights Reserved.
 //
 // Authors: wjr@google.com (William Rucklidge),
 //          keir@google.com (Keir Mierle),
@@ -40,9 +40,11 @@
 
 #include "ceres/cost_function.h"
 #include "ceres/dynamic_numeric_diff_cost_function.h"
+#include "ceres/internal/disable_warnings.h"
 #include "ceres/internal/eigen.h"
+#include "ceres/internal/export.h"
 #include "ceres/internal/fixed_array.h"
-#include "ceres/local_parameterization.h"
+#include "ceres/manifold.h"
 #include "glog/logging.h"
 
 namespace ceres {
@@ -56,27 +58,27 @@
 //   ------------------------------------  <  relative_precision
 //   max(J_actual(i, j), J_numeric(i, j))
 //
-// where J_actual(i, j) is the jacobian as computed by the supplied cost
-// function (by the user) multiplied by the local parameterization Jacobian
-// and J_numeric is the jacobian as computed by finite differences, multiplied
-// by the local parameterization Jacobian as well.
+// where J_actual(i, j) is the Jacobian as computed by the supplied cost
+// function (by the user) multiplied by the manifold Jacobian and J_numeric is
+// the Jacobian as computed by finite differences, multiplied by the manifold
+// Jacobian as well.
 //
 // How to use: Fill in an array of pointers to parameter blocks for your
 // CostFunction, and then call Probe(). Check that the return value is 'true'.
 class CERES_EXPORT GradientChecker {
  public:
-  // This will not take ownership of the cost function or local
-  // parameterizations.
+  // This will not take ownership of the cost function or manifolds.
   //
   // function: The cost function to probe.
-  // local_parameterizations: A vector of local parameterizations for each
-  // parameter. May be NULL or contain NULL pointers to indicate that the
-  // respective parameter does not have a local parameterization.
+  //
+  // manifolds: A vector of manifolds for each parameter. May be nullptr or
+  // contain nullptrs to indicate that the respective parameter blocks are
+  // Euclidean.
+  //
   // options: Options to use for numerical differentiation.
-  GradientChecker(
-      const CostFunction* function,
-      const std::vector<const LocalParameterization*>* local_parameterizations,
-      const NumericDiffOptions& options);
+  GradientChecker(const CostFunction* function,
+                  const std::vector<const Manifold*>* manifolds,
+                  const NumericDiffOptions& options);
 
   // Contains results from a call to Probe for later inspection.
   struct CERES_EXPORT ProbeResults {
@@ -87,11 +89,11 @@
     Vector residuals;
 
     // The sizes of the Jacobians below are dictated by the cost function's
-    // parameter block size and residual block sizes. If a parameter block
-    // has a local parameterization associated with it, the size of the "local"
-    // Jacobian will be determined by the local parameterization dimension and
-    // residual block size, otherwise it will be identical to the regular
-    // Jacobian.
+    // parameter block size and residual block sizes. If a parameter block has a
+    // manifold associated with it, the size of the "local" Jacobian will be
+    // determined by the dimension of the manifold (which is the same as the
+    // dimension of the tangent space) and residual block size, otherwise it
+    // will be identical to the regular Jacobian.
 
     // Derivatives as computed by the cost function.
     std::vector<Matrix> jacobians;
@@ -114,20 +116,20 @@
   };
 
   // Call the cost function, compute alternative Jacobians using finite
-  // differencing and compare results. If local parameterizations are given,
-  // the Jacobians will be multiplied by the local parameterization Jacobians
-  // before performing the check, which effectively means that all errors along
-  // the null space of the local parameterization will be ignored.
-  // Returns false if the Jacobians don't match, the cost function return false,
-  // or if the cost function returns different residual when called with a
-  // Jacobian output argument vs. calling it without. Otherwise returns true.
+  // differencing and compare results. If manifolds are given, the Jacobians
+  // will be multiplied by the manifold Jacobians before performing the check,
+  // which effectively means that all errors along the null space of the
+  // manifold will be ignored.  Returns false if the Jacobians don't match, the
+  // cost function return false, or if a cost function returns a different
+  // residual when called with a Jacobian output argument vs. calling it
+  // without. Otherwise returns true.
   //
   // parameters: The parameter values at which to probe.
   // relative_precision: A threshold for the relative difference between the
   // Jacobians. If the Jacobians differ by more than this amount, then the
   // probe fails.
   // results: On return, the Jacobians (and other information) will be stored
-  // here. May be NULL.
+  // here. May be nullptr.
   //
   // Returns true if no problems are detected and the difference between the
   // Jacobians is less than error_tolerance.
@@ -140,11 +142,13 @@
   GradientChecker(const GradientChecker&) = delete;
   void operator=(const GradientChecker&) = delete;
 
-  std::vector<const LocalParameterization*> local_parameterizations_;
+  std::vector<const Manifold*> manifolds_;
   const CostFunction* function_;
   std::unique_ptr<CostFunction> finite_diff_cost_function_;
 };
 
 }  // namespace ceres
 
+#include "ceres/internal/reenable_warnings.h"
+
 #endif  // CERES_PUBLIC_GRADIENT_CHECKER_H_