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...Riemannian geometry contents chapter smooth manifolds tangent vectors cotangent and tensors the bundle of a manifold vector elds covector tensor n forms metric three model geometries connections geodesics parallel translation along curves connection on submanifolds pull back in exponential map normal coordinates riemann distance function curvature ricci scalar einstein metrics sectional jacobi comparison theorems space times multilinear algebra inner product spaces coordinate expressions non euclidean hyperbolic plane bibliography...