Course Archives    Theoretical Statistics and Mathematics Unit
Course: Differential Geometry II
Time: Currently not offered
Level: Postgraduate
Past Exams

Syllabus: 1. A quick review of tensors, alternating forms, manifolds, immersion, submersion and submanifolds.

2. Tangent bundle, vector bundles, vector fields, flows and the fundamental theorem of ODE. Embedding in Euclidean space, tubular neighbourhood. Differential forms and integration, Stoke's theorem. Transversality, Riemann metrics, Riemannian connection on Riemannian manifolds, Gauss-Bonnet theorem. Parallel transport, geodesics and geodesic completeness, the theorem of Hopf- Rinow.

Suggested Texts :

1. F. W. Warner, Foundations of differentiable manifolds and Lie groups, GTM (94), Springer- Verlag (1983).

2. S. Helgason, Differential geometry, Lie groups, and symmetric space, Graduate Studies in Mathematics (34), AMS (2001).

3. W.M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, Academic Press (1975); Elsevier (2008).

4. J.M. Lee, Riemannian Manifolds: An Introduction to Curvature, GTM (176), Springer (1997).

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Past Exams
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Supplementary and Back Paper

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