Diff Geo II
WS 2008/09


Equivalent to the basic course
"Analysis and Geometry on Manifolds"

0230 L 218 / 219
Thursdays 14-16 and 16-18 in room MA 749
Wednesdays 14-16 in room MA 850
Course information is online at
John M. Sullivan, MA 318, tel 314-29279
Office Hours (Sullivan):
Tuesdays 11:45-13:00, or by appointment
Pasquale Zito
Office Hours (Zito):
Mondays 14:15-15:45 in MA 843
Analysis, elementary topology
Course work:
weekly homework assignments,
two written tests, take-home final exam
Primary Textbook:
Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd Ed, Academic Press
Additional Textbooks:
Morgan, Riemannian Geometry: A Beginner's Guide, 2nd Ed, A K Peters
Bishop and Goldberg, Tensor Analysis on Manifolds, Dover
Milnor, Topology from the Differentiable Viewpoint, U P Virginia
Spivak, Calculus on Manifolds, Benjamin/Cummings
This is a first course in manifolds and global analysis, which will present the basic tools for those interested in, or curious about, differential geometry or global analysis, or those who want to apply differentiial geometric methods in other areas such as PDE, topology, mathematical physics, and dynamical systems. The course will cover the following topics:
Differentiable manifolds, implicit function theorem, rank theorem, tangent spaces, tangent bundles, vector bundles.
Calculus on manifolds:
Vector fields, flows, Lie bracket, Lie derivatives, Frobenius theorem.
Differential forms:
Differential forms, exterior calculus, orientability, Poincaré lemma, deRham complex.
Integration theory:
Stokes' theorem.
Riemannian geometry:
Riemannian metrics, distance, first variation and geodesics, Riemannian connection, curvature, connections on vector bundles.