هندسه.. منیفولدهای هموار، هندسه شبه ریمانی، منیفولدهای اوسرمن

Contents Smooth manifolds and maps Historical introduction Topological manifolds Topological properties of manifolds Smooth manifolds Quotient manifolds Smooth maps Diffeomorphisms Partitions of unity Tangent vectors and maps Tangent vectors Tangent maps Submersions and immersions Submanifolds Vector fields and bundles Vector fields Global tangent maps Vector bundles Local and global frames Vector fields on a sphere Tensor fields Covector fields Tensor fields Tensor fields derivations Pseudo-Riemannian metric Scalar products Null vectors Pseudo-Riemannian manifolds Pullback of metric tensors Musical isomorphisms Model spaces Length and distance Connection Covariant derivatives Levi-Civita connection Parallel transport Geodesics Exponential map Geodesics and minimizing curves Completeness Curvature Curvature tensor fields Algebraic curvature tensors Sectional curvature Constant sectional curvature Ricci curvature The Ricci identities Local isometries More pseudo-Riemannian geometry Jacobi fields Pseudo-Riemannian submanifolds Symmetric spaces Osserman conditions Osserman conditions Osserman manifolds examples Osserman algebraic curvature tensor Einstein, zwei-stein, ... Lorentzian zwei-stein Zwei-stein submanifolds Duality principle Duality principle Quasi-Clifford curvature tensors Total duality Four-dimensional zwei-stein Converse problem Osserman perturbations Osserman tensors and manifolds Simple-root Osserman tensors Riemannian Osserman tensors Schur problems One-root manifolds Two-root Osserman manifolds Two-root Riemannian tensors Two-root Riemannian manifolds Proportionality principle Appendix Eigen-structure of linear operators Topology Analysis Algebra Number theory Bibliography Index