Morgan Frank. Riemannian Geometry: A Beginner's Guide

Jones and Bartlett Publ., England, 1993. — 121 p. — ISBN: 0-86720-242-4.The complicated formulations of Riemannian geometry present a daunting aspect to the student This little book focuses on the central concept-curvature It gives a naive treatment of Riemannian geometry, based on surfaces in Rn rather than on abstract Riemannian manifolds. The more ophIstIcated mtnnslC formulas folIow naturalIy. Later chapters treat hyperbobc geometry, general relatIVIty, global geometry, and some current research on energy-mlmmlzmg curves and the lsopenmetnc problem. Proofs, when given at all, emphasize the main ideas and suppress the details that otherwise might overwhelm the student.Curves In Rn
Surfaces In R3
M-Dimensional Surfaces In Rn
Intrinsic Riemannian Geometry
General Relativity
The Gauss-Bonnet Theorem
Geodesics And Global Geometry
General Norms