Riemannian Geometry and Geometric Analysis (3rd ed.)

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