Differential and Riemannian Geometry |
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Contents
CHAPTER I | 1 |
CHAPTER II | 19 |
TENSOR CALCULUS AND RIEMANNIAN GEOMETRY | 79 |
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affine connection analytic angle arc length assume auto-parallel Christoffel symbols circle components conformal mapping const constant curvature coordinate system covariant derivative covariant differentiation curvature tensor defined developable surface differential equations differential geometry direction element of arc ellipsoid Euclidean space Exercise following result formulas function Gauss Gaussian curvature geodesic curvature geodesic curves geodesic parallelism given hence Hint holonomy group indicatrix initial conditions integral invariant linear connection minimal surfaces moving trihedron neighborhood obtain orthogonal parallel displacement parallel vectors parameter transformation Proof properties quantities Riemannian curvature Riemannian geometry Riemannian metric Riemannian space satisfy similarity mapping solution space curves spaces of constant sphere spherical straight lines surfaces of revolution tangent plane tangent space tangent vectors Theorem theory of surfaces trajectories unit vector V₂ vanishes vector field vector space x(uš дхі