 
Summary: Math 240B
Course Outline and Information
Winter 2012
Lecture: MWF 9:00 9:50;
Text: M. P. do Carmo, Riemannian Geometry. Birkhauser, 1992.
Instructor: Guofang Wei, South Hall 6503
email: wei@math.ucsb.edu
Office hours: MWF 12:001:00pm or by appointment
Homework: There will be about five homework assignments, which will also be
posted on my web page http://www.math.ucsb.edu/wei.
Grades: 25% homework; 30% midterm (take home); 45% final (take home)
Course Material: Chapters 18 of book by M. P. do Carmo
Course outline: We will first introduce the basic concepts: Riemannian metric,
Riemannian connection, geodesics, and curvature. A lot of geometrics information
can be derived from our understanding of geodesic and the interaction of geodesics
and curvature is our primary concern. At the most fundamental level this interaction
is exhibited by what are called Jacobi fields.
We then start the study of global geometry with another very important concept:
completeness. Its characterization by the so called HopfRinow theorem is the most
fundamental result in Riemannain geometry. After looking into spaces of constant
