02705nam a22004095i 4500978-3-662-03118-6cr nn 008mamaa130321s1995 gw : s :::: 0:eng d9783662031186ENGDEQA641-670516.36Online resource: SpringerJost, Jürgen.1956-Riemannian Geometry and Geometric Analysis[EBook]by Jürgen Jost.Berlin, HeidelbergSpringer1995.XI, 404 pagesonline resource.textonline resourceUniversitext,0172-59391. Foundational Material -- 2. De Rham Cohomology and Harmonic Differential Forms -- 3. Parallel Transport, Connections, and Covariant Derivatives -- 4. Geodesics and Jacobi Fields -- A Short Survey on Curvature and Topology -- 5. Morse Theory and Closed Geodesics -- 6. Symmetric Spaces and Kähler Manifolds -- 7. The Palais-Smale Condition and Closed Geodesics -- 8. Harmonic Maps -- Appendix A: Linear Elliptic Partial Differential Equations -- A.1 Sobolev Spaces -- A.2 Existence and Regularity Theory for Solutions of Linear Elliptic Equations -- Appendix B: Fundamental Groups and Covering Spaces.This textbook introduces techniques from nonlinear analysis at an early stage. Such techniques have recently become an indispensable tool in research in geometry, and they are treated here for the first time in a textbook. Topics treated include: Differentiable and Riemannian manifolds, metric properties, tensor calculus, vector bundles; the Hodge Theorem for de Rham cohomology; connections and curvature, the Yang-Mills functional; geodesics and Jacobi fields, Rauch comparison theorem and applications; Morse theory (including an introduction to algebraic topology), applications to the existence of closed geodesics; symmetric spaces and Kähler manifolds; the Palais-Smale condition and closed geodesics; Harmonic maps, minimal surfaces.Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)Mathematical analysis.Analysis (Mathematics).System theory.Differential GeometryCalculus of variations.Manifolds (Mathematics).Complex manifolds.Systems Theory, Control.Calculus of Variations and Optimal Control; Optimization.Mathematical Methods in Physics.SpringerLink (Online service)Universitext,http://dx.doi.org/10.1007/978-3-662-03118-6