A Comprehensive Introduction to Differential Geometry, Volume 1

ax¹ called 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 exp tY fibre finite function f geodesic 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 U₁ unique V₁ vector bundle vector field vector space w₂ θα Ρε Σα χε ду дх