Riemannian Geometry and Geometric Analysis

Jürgen Jost is Codirector of the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, an Honorary Professor at the Department of Mathematics and Computer Sciences at Leipzig University, and an External Faculty Member of the Santa Fe Institute for the Sciences of Complexity, New Mexico, USA. He is the author of a number of further Springer textbooks including Postmodern Analysis (1997, 2002, 2005), Compact Riemann Surfaces (1997, 2002, 2006), Partial Differential Equations (2002, 2007, 2013), Differentialgeometrie und Minimalflächen (1994, 2007, 2014, with J. Eschenburg), Dynamical Systems (2005), Mathematical Concepts (2015), as well as several research monographs, such as Geometry and Physics (2009), and many publications in scientific journals.

• 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.

“The present volume ends with two appendices (on linear elliptic partial differential equations and topological results about fundamental groups and covering spaces) and a rich bibliography of 454 items, including some classical books and papers. All the material, written in a clear and precise style, is carefully developed, many examples supporting the understanding. In the reviewer’s opinion, this is an excellent book, a very useful addition to any good library.” (Gabriel Eduard Vilcu, zbMATH 1380.53001, 2018)