Differential Manifolds |
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affine connection algebra anti-derivation B₂ bilinear bundle called compact components coordinate neighborhood coordinate system Corollary corresponding covectors definition denote derivatives differentiable manifold differentiable mapping differentiable structure differential forms differential system dimension du¹ dual bases element endomorphism equations exists exterior algebra exterior differential exterior polynomials field of type finite number form of degree formula function f functions of class geodesic given group of holonomy Hence homeomorphism induces isometry Lemma linear differential forms linear map linear subspace linearly independent local coordinates map f Moreover multiplication normal coordinates open subset parametrized curve properties prove r-vectors restrict Riemann manifold Riemann metric satisfying the conditions sectional curvature segment Sijkl spherical structure of class submanifold Suppose tangent space tangent vectors tensor field tensor product Theorem 2.1 topology vector space zero