From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry, e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. It is a good introduction to Riemannian geometry. The book is made more interesting by the perspectives in various sections. where the author mentions the history and development of the material and provides the reader with references." Math. Reviews. The 2nd ed. includes new material on Ginzburg-Landau, Seibert-Witten functionals, spin geometry, Dirac operators.
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Auflage
Sprache
Verlagsort
Verlagsgruppe
Illustrationen
ISBN-13
978-3-662-22385-7 (9783662223857)
DOI
10.1007/978-3-662-22385-7
Schweitzer Klassifikation
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 Kähler Manifolds.- 7. The Palais-Smale Condition and Closed Geodesics.- 8. Harmonic Maps.- 9. Variational Problems from Quantum Field Theory.- Appendix A: Linear Elliptic Partial Differential Equation.- A.1 Sobolev Spaces.- A.2 Existence and Regularity Theory for Solutions of Linear Elliptic Equations.- Appendix B: Fundamental Groups and Covering Spaces.
