Our aim is twofold, as announced by our subtitle. The first is to introduce
the various concepts and tools of Riemannian geometry in the most natural
way; or more, to demonstrate that one is practic . . . . .
Contents: Introduction to manifolds; functions of several variables and mappings; differentiable manifolds and submanifolds; vector fields on a manifolds; tensors and tensors fields on manifolds; inte . . . . .
Contents: The Simplest Concepts and the Object of the Investigation; Angle; Approximation by Polyhedral Metrics; Metrics Admitting Approximation by Polyhedral Metrics; Curvature; Rotation of Curves. P . . . . .
This book represents course notes for a one semester course at the undergraduate
level giving an introduction to Riemannian geometry and its principal physical
application, Einsteinís theory of gene . . . . .
Contents: Literatur; Riemannsche Metrik
Die Levi-Civita-Ableitung; Innere Metrik; Geodatische; Geodatische und Ku rzeste; Geodatische Konvexitat; Der Satz von Hopf-Rinow; Parallelverschiebung; Der . . . . .