Riemannian Geometry and Geometric Analysis by Jürgen Jost
English | PDF | 2005 | 574 Pages | ISBN : 3540259074 | 4.16 MB
Riemannian geometry is characterized, and research is oriented towards and shaped by concepts (geodesics, connections, curvature, …) and objectives, in particular to understand certain classes of (compact) Riemannian manifolds defined by curvature conditions (constant or positive or negative curvature, …). By way of contrast, geometric analysis is a perhaps somewhat less system- atic collection of techniques, for solving extremal problems naturally arising in geometry and for investigating and characterizing their solutions. It turns out that the two fields complement each other very well; geometric analysis offers tools for solving difficult problems in geometry, and Riemannian geom- etry stimulates progress in geometric analysis by setting ambitious goals.