Riemannian Geometry and Geometric Analysis

• Main Author: Jost, Jürgen (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Edition: 7th ed. 2017.
• Series: Universitext,
• Subjects: Mathematics.; Differential geometry.; Physics.; Differential Geometry.; Theoretical, Mathematical and Computational Physics.

This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; t...

Table of Contents:

• 1 Riemannian Manifolds
• 2 Lie Groups and Vector Bundles
• 3 The Laplace Operator and Harmonic Differential Forms
• 4 Connections and Curvature
• 5 Geometry of Submanifolds
• 6 Geodesics and Jacobi Fields
• A Short Survey on Curvature and Topology
• 7 Symmetric Spaces and Kähler Manifolds
• 8 Morse Theory and Floer Homology
• 9 Harmonic Maps between Riemannian Manifolds
• 10 Harmonic Maps from Riemann Surfaces
• 11 Variational Problems from Quantum Field Theory
• A Linear Elliptic Partial Differential Equations
• B Fundamental Groups and Covering Spaces
• Bibliography
• Index.