Tensor Analysis on Manifolds |
Contents
Chapter 0Set Theory and Topology | 1 |
Chapter 1Manifolds | 19 |
Chapter 2Tensor Algebra | 59 |
Copyright | |
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Common terms and phrases
affine algebra atlas b₁ bilinear form called cartesian compact components connexion constant contravariant coordinate expression coordinate map coordinate system coordinate vector coordinate vector fields covariant critical points defined definition denoted derivatives diffeomorphism differential equations dimension domain dual basis dx¹ e₁ elements equivalent example finite number follows formula function f geodesic given h-dimensional hamiltonian hence integral curve integral submanifold invariant inverse isomorphism linear combination linear function linearly independent manifold matrix metric nonsingular nonzero notation obtain open set operator oriented orthonormal basis p-chain p-cube p-form P₁ parametrization Problem Proof Proposition respect riemannian riemannian metric scalar Section semi-riemannian skew-symmetric structure submanifold subset subspace tangent space tensor field tensor of type Theorem topological space topology unique v₁ variables vector field vector space