## Diff Geo II WS 2010

 TU LV-Nr:3236 L 218 BMS Basic Course:Analysis and Geometry on Manifolds Lectures:Tue 14-16, Thu 10-12 in room MA 650 Tutorial:Wed 12-14 in room MA 650 Professor:John M. Sullivan, MA 318, tel. 314-29279 sullivan@math.tu-berlin.de, office hours Tue 11:30-12:30 or by appointment Assistant:David Chubelaschwili, office hours TBA Prerequisites:Analysis, elementary topology
 WWW: Course information is online at www.math.tu-berlin.de/~sullivan/L/10W/DG2/ Course work:weekly homework assignments, one written test, oral final exam Textbooks: Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd Ed, Academic Press Bröcker and Jänich, Intro to Differential Topology / Einführung in die Differentialtopologie, CUP / Springer Kühnel, Differential Geometry / Differentialgeometrie, AMS / Vieweg Warner, Foundations of Differentiable Manifolds and Lie Groups, GTM 94, Springer 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 Sharpe, Differential Geometry, GTM 166, Springer Outline: 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: Manifolds: 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.