| Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
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Course: Differential Geometry II Instructor: Aniruddha C Naolekar Room: G25 Level: Postgraduate Time: Currently offered |
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| Syllabus Past Exams Syllabus: [Prerequisite: Differential Geometry I] • A quick review of tensors, alternating forms, manifolds, immersion, submersion and submanifolds. • Tangent bundle, vector bundles, vector fields, flows and the fundamental theorem of ODE. Riemann metrics, Riemannian connection on Riemannian manifolds. Parallel transport, geodesics and geodesic completeness, the theorem of Hopf-Rinow. • Time permitting: Gauss-Bonnet theorem. Suggested Texts : (a) F. W. Warner, Foundations of differentiable manifolds and Lie groups, GTM (94), Springer-Verlag (1983). (b) S. Helgason, Differential geometry, Lie groups, and symmetric space, Graduate Studies in Mathematics (34), AMS (2001). (c) W.M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, Academic Press (1975); Elsevier (2008). (d) J.M. Lee, Riemannian Manifolds: An Introduction to Curvature, GTM (176), Springer (1997). Evaluation:
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[ Semester Schedule ][ SMU ] [Indian Statistical Institute] |