MATHEMATICS 567- RIEMANNIAN GEOMETRY

FALL 2008- ALEX FREIRE (Ayres 207A)

This is an introductory graduate-level course; the prerequisite is one year of advanced calculus.
No prior familiarity with differentiable manifolds or elementary differential geometry (curves and surfaces)
will be assumed.  This course will cover basic concepts of wide applicability for anyone interested in differential geometry,
geometric topology, partial differential equations or general relativity (including first-year graduate students).

TEXT:  Riemannian Geometry , by Manfredo P. do Carmo (Birkhauser 1992) (required)
List price: $49.95 (the bookstore will order it, or you can buy it online).

Table of contents (Amazon.com)
(This will give you an idea of the main topics in the course)

Time/place: 12:40-1:55 TR, Ayres 209A

Recommended background reading (if you have time this summer):

F. Warner, Foundations of differentiable manifolds and Lie groups
M. do Carmo, Differential geometry of curves and surfaces

GRADING: based on weekly problem sets

REMARK: The intended audience for this course are graduate students in mathematics
(research-oriented). Differential geometry is also important in many applications
(computer graphics, imaging, engineering, architecture).  For those interested in applications,
a better course is Math 462 (which can be taken for graduate credit). Indeed the overlap between the
two courses will be minimal, and Math 462 will be of interest not only to engineers and physicists,
but also for mathematics students. There is a link to that course from my web page, with more details.