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- catalog abstract "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.".
- catalog contributor b8194452.
- catalog created "c1995.".
- catalog date "1995".
- catalog date "c1995.".
- catalog dateCopyrighted "c1995.".
- catalog description "1. 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 Kahler Manifolds -- 7. The Palais-Smale Condition and Closed Geodesics -- 8. Harmonic Maps -- Appendix A: Linear Elliptic Partial Differential Equations -- Appendix B: Fundamental Groups and Covering Spaces.".
- catalog description "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.".
- catalog extent "xi, 401 p. ;".
- catalog hasFormat "Riemannian geometry and geometric analysis.".
- catalog identifier "0387571132 (New York : acid-free)".
- catalog identifier "3540571132 (Berlin : acid-free)".
- catalog isFormatOf "Riemannian geometry and geometric analysis.".
- catalog isPartOf "Universitext".
- catalog issued "1995".
- catalog issued "c1995.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Riemannian geometry and geometric analysis.".
- catalog subject "516.3/73 20".
- catalog subject "Cell aggregation Mathematics.".
- catalog subject "Geometry, Riemannian.".
- catalog subject "Global analysis (Mathematics).".
- catalog subject "Global differential geometry.".
- catalog subject "Mathematical optimization.".
- catalog subject "Mathematical physics.".
- catalog subject "Mathematics.".
- catalog subject "QA649 .J67 1995".
- catalog subject "Systems theory.".
- catalog tableOfContents "1. 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 Kahler Manifolds -- 7. The Palais-Smale Condition and Closed Geodesics -- 8. Harmonic Maps -- Appendix A: Linear Elliptic Partial Differential Equations -- Appendix B: Fundamental Groups and Covering Spaces.".
- catalog title "Riemannian geometry and geometric analysis / Jürgen Jost.".
- catalog type "text".