InhaltsangabeFinite-Dimensional Vector Spaces and Linear Mappings.- Tensor Algebra.- Tensor Analysis on a Differentiable Manifold.- Differentiable Manifolds with Connections.- Riemannian and Pseudo-Riemannian Manifolds.- Special Riemannian and Pseudo-Riemannian Manifolds.- Hypersurfaces, Submanifolds, and Extrinsic Curvature.

Finite- Dimensional Vector Spaces and Linear Mappings.- Fields.- Finite-Dimensional Vector Spaces.- Linear Mappings of a Vector Space.- Dual or Covariant Vector Space.- Tensor Algebra.- The Second Order Tensors.- Higher Order Tensors.- Exterior or Grassmann Algebra.- Inner Product Vector Spaces and the Metric Tensor.- Tensor Analysis on a Differentiable Manifold.- Differentiable Manifolds.- Vectors and Curves.- Tensor Fields over Differentiable Manifolds.- Differential Forms and Exterior Derivatives.- Differentiable Manifolds with Connections.- The Affine Connection and Covariant Derivative.- Covariant Derivatives of Tensors along a Curve.- Lie Bracket, Torsion, and Curvature Tensor.- Riemannian and Pseudo-Riemannian Manifolds.- Metric, Christoffel, Ricci Rotation.- Covariant Derivatives.- Curves, Frenet-Serret Formulas, and Geodesics.- Special Coordinate Charts.- Speical Riemannian and Pseudo-Riemannian Manifolds.- Flat Manifolds.- The Space of Constant Curvature.- Extrinsic Curvature.