A Comprehensive Introduction to Differential Geometry, Volume 1Publish or Perish, Incorporated, 1975 - Geometry, Differential |
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ax¹ called Chapter choose clearly compact support components compute connected consider continuous coordinate system coordinate system x,U COROLLARY countable covariant critical point define definition denote diffeomorphism differential equations dt dt dx¹ element example exp tY fibre finite function f geodesic hence homeomorphic identity inner product integral curve integral manifold isomorphism k-form left invariant Lemma Let f Lie algebra Lie group linear M₁ M₂ manifold-with-boundary map f matrix Möbius strip n-dimensional n-manifold neighborhood obtain one-one open set order isomorphic orientation preserving Problem Proof Proposition prove Riemannian metric satisfies sequence Show structure subgroup submanifold subset subspace Suppose tangent bundle tangent vector tensor field Theorem topology trivial U₁ unique V₁ V₂ vector bundle vector field vector space w₂ Ρε ΣΑ χε