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This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been re

Differential geometry. Global analysis --- Calculus of tensors --- Manifolds (Mathematics) --- Relativity (Physics) --- Semi-Riemannian geometry --- #WPLT:dd.Prof.F.Symons --- 514.84 --- 515.165 --- 517.518.12 --- Geometry, Differential --- Topology --- 517.518.12 Theory of integration. Riemann integral. Lebesgue integral. Stieltjes integral --- Theory of integration. Riemann integral. Lebesgue integral. Stieltjes integral --- 515.165 Topology of smooth manifolds provided with additional structure. Kähler manifolds. Riemann manifolds --- Topology of smooth manifolds provided with additional structure. Kähler manifolds. Riemann manifolds --- 514.84 Geometric methods in quantum mechanics and in the theory of elementary particles --- Geometric methods in quantum mechanics and in the theory of elementary particles --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Gravitation --- Nonrelativistic quantum mechanics --- Space and time --- Pseudo-Riemannian geometry --- Géométrie différentielle --- Relativité (physique) --- Geometry, Riemannian --- Riemann, Géométrie de --- Variétés (Mathématiques) --- Calcul tensoriel --- Relativité (Physique) --- Geometry, Riemannian. --- Calculus of tensors. --- Manifolds (Mathematics). --- Relativity (Physics). --- Semi-Riemannian geometry. --- Riemann geometry --- Riemannian geometry --- Generalized spaces --- Geometry, Non-Euclidean --- Géometrie différentielle globale --- Géometrie différentielle