An Introduction to Differentiable Manifolds and Riemannian GeometryAn Introduction to Differentiable Manifolds and Riemannian Geometry |
Contents
| 1 | |
| 20 | |
Chapter III Differentiable Manifolds and Submanifolds | 51 |
Chapter IV Vector Fields on a Manifold | 106 |
Chapter V Tensors and Tensor Fields on Manifolds | 176 |
Chapter VI Integration on Manifolds | 229 |
Chapter VII Differentiation on Riemannian Manifolds | 297 |
Chapter VIII Curvature | 365 |
| 417 | |
| 423 | |
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An Introduction to Differentiable Manifolds and Riemannian ..., Volume 120 William M. Boothby No preview available - 2003 |
Common terms and phrases
algebra basis bi-invariant Co-vector field compact completes the proof components constant coordinate frames coordinate neighborhood Corollary corresponding covariant tensor covering curvature defined definition denote derivative diffeomorphism differentiable dimension domain of integration dp/dt E₁ equations equivalent Euclidean space example Exercise F₁ fact formula functions geodesic geometry given Gl(n homeomorphism homotopy identity imbedding inner product integral curve isometry isomorphism k₁ left-invariant Lemma Let F Lie group Lie group G linear map M₁ mapping F matrix notation one-parameter subgroup one-to-one open set open subset oriented orthogonal orthonormal parameter plane properties prove real numbers regular submanifold Riemannian manifold Riemannian metric Section Show submanifold subspace suppose surface symmetric tangent space tangent vector tensor field Theorem Let topology U₁ uniquely determined V₁ vector field vector space zero дх