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Chapter OSet Theory and Topology
Chapter 2Tensor Algebra
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affine algebra atlas bilinear form called cartesian coefficients compact components compute connected connexion constant contravariant coordinate expression coordinate map coordinate neighborhood coordinate system coordinate vector coordinate vector fields covariant critical points cube curvature defined definition denoted derivatives determinant diffeomorphism differential equations dimension domain dual basis elements energy-critical equivalent euclidean example finite number follows formula geodesic given hamiltonian Hausdorff space hence integral curve integral submanifold invariant inverse isomorphism jacobian linear combination linear function linearly independent manifold matrix metric nonsingular nonzero notation obtain open set operator oriented orthonormal basis p-cube p-form parametrization Problem Proof Proposition real-valued function respect restriction riemannian riemannian metric scalar Section semi-riemannian skew-symmetric structure submanifold subset subspace surface tangent space tensor field tensor of type Theorem topological space topology torus unique values variables vector field vector space