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...Abrief introduction to semi riemannian geometry and general relativity hans ringstr om may contents scalar product spaces products orthonormal bases adapted subspaces causality for lorentz manifolds metrics pullback isometries musical isomorphisms causal notions in warped existence of distance function relevance the euclidean minkowski levi civita connection parallel translation geodesics variational characterization curvature tensor calculating ricci divergence gradient laplacian computing covariant derivative elds a eld an example calculation coecients components sphere hyperbolic space i ii upper half model...