Comments:

72 pages, 2005

Abstract:

Author's specified contents: "Contents 1 Smooth Manifolds 3 1.1 Smooth Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Submanifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Smooth Mappings between Smooth Manifolds . . . . . . . . . 5 1.4 Bump Functions and Partitions of Unity . . . . . . . . . . . . 5 2 Tangent Spaces 7 2.1 Derivatives of Smooth Maps . . . . . . . . . . . . . . . . . . . 12 2.2 Vector Fields on Smooth Manifolds . . . . . . . . . . . . . . . 12 2.3 The Lie Bracket . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3 Affine Connections on Smooth Manifolds 16 3.1 Vector Fields along Smooth Maps . . . . . . . . . . . . . . . . 23 3.2 Covariant Differentiation of Vector Fields along Curves . . . . 24 3.3 Vector Fields along Parameterized Surfaces . . . . . . . . . . . 25 4 Riemannian Manifolds 28 4.1 The Levi-Civita Connection . . . . . . . . . . . . . . . . . . . 30 5 Geometry of Surfaces in R3 36 6 Geodesics in Riemannian Manifolds 46 6.1 Length-Minimizing Curves in Riemannian Manifolds . . . . . 49 6.2 Geodesic Spheres and Gauss’ Lemma . . . . . . . . . . . . . . 52 7 Complete Riemannian Manifolds 55 7.1 Local Isometries and Covering Maps . . . . . . . . . . . . . . 58. "

Rights:

Copyright@2005 by David R. Wilkins http://www.maths.tcd.ie/~dwilkins/Courses/425/RiemGeom.pdf

Download:

RiemGeom.pdf
RiemGeom.pdf.1
RiemGeomWilkins85p.pdf

No messages.