Riemannian geometry and geometric analysis
Jost, Jürgen
Riemannian geometry and geometric analysis - 7th ed. - Switzerland : Springer, 2017. - xiv, 697p. : 19 illustrations, 4 illustrations in color. - Universitext 0172-5939 .
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; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research.
The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes newmaterial, for instance on symplectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature.
9783319618593
Differential geometry
Mathematical physics
Riemannian geometry
Riemannian manifolds
Lie groups
Symplectic geometry
Kähler manifolds
Morse theory
Floer homology
514.764.21 / JOS-R
Riemannian geometry and geometric analysis - 7th ed. - Switzerland : Springer, 2017. - xiv, 697p. : 19 illustrations, 4 illustrations in color. - Universitext 0172-5939 .
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; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research.
The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes newmaterial, for instance on symplectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature.
9783319618593
Differential geometry
Mathematical physics
Riemannian geometry
Riemannian manifolds
Lie groups
Symplectic geometry
Kähler manifolds
Morse theory
Floer homology
514.764.21 / JOS-R
