## Lectures on tensor calculus and differential geometry |

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### Contents

LINEAR VECTOR SPACES | 1 |

METRIC VECTOR SPACES | 14 |

TENSORS | 42 |

Copyright | |

6 other sections not shown

### Common terms and phrases

angle arbitrary vectors arc length basis xK bivector called Christoffel symbols conditions of integrability congruence consequence consider constant Riemannian curvature contravariant coordinate vector cos2 covariant components covariant differentiation curve x(s denote differential equations dimension eigenvalues eigenvector expression fact finite dimensional flat follows formula geodesic curve given curve given point Hence hyperplane hypersphere hypersurface introduce line of curvature linear operator linearly independent metric space metric tensor metric vector space multilinear form multiplying both members norm normal number space obtained orthogonal orthonormal frame osculating parameter point space principal curvatures principal directions real numbers referred relation replace Riccian Riemannian curvature scalar invariant second fundamental tensor space spanned Suppose symmetric taking account tangent space tangent vector tensor of valency transformation Transvecting uniquely determined unit vector values vanishes variables vector function vector plane w-dimensional whence wish write x(qK zero vector