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RIEMANNIAN GEOMETRY (PhD)

Lecture Topic : RIEMANNIAN GEOMETRY (PhD)

Prerequisites : Riemannian Geometry (M2); Algebraic Topology (M1); Manifold Theory (M1); Differential Forms (M1); Lie Groups (M1); Cohomology (M2);

Recommended Text(s) :

“Riemannian Geometry”, 2nd Edn., Graduate Texts in Mathematics xxx , Peter Petersen, Springer, 2010.

Approx price new on Amazon.com (hard copy) : $36

Approx price second hand on Amazon.com (hard copy) : $29

Availability free on eMule.com (e-format) : Yes

eMule search key word(s) : Riemannian Geometry, Petersen

Lectures and Links :

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Lecture 1  (link)

Ch.1   Riemannian Metrics

Ch.2   Curvature

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Lecture 2  (link)

Ch.3   Examples

Ch.4   Hypersurfaces

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Lecture 3  (link)

Ch.5   Geodesics and Distance

Ch.6   Sectional Curvature Comparison I

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Lecture 4  (link)

Ch.7   The Bochner Technique

Ch.8   Symmetric Spaces and Holonomy

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Lecture 5   (link)

Ch.9     Ricci Curvature Comparison

Ch.10   Convergence

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Lecture 6   (link)

Ch.11   Sectional Curvature Comparison II

Appendix : de Rham Cohomology

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Links to Other Lecturers on this Topic :

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