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Course Descriptions

16:640:532 - Introduction to Differential Geometry

Jian Song

Text: Riemannian geometry: A metric entrance" by Karsten Grove

Prerequisites: None


This is an introduction course for Riemannian geometry and differential geometry. In this course, we will NOT assume a knowledge related to a manifold (tangent bundle, connection, etc), which will be introduced during the course. The following are basic contents of this course:

  1. Riemannian Length and Distance
  2. Geodesics
  3. The First Variation of Arc Length
  4. The Levi-Civita Connection
  5. The Exponential Maps
  6. Isometries
  7. Jacobi Fields and Curvature
  8. Curvature Identities
  9. Second Variation of Arc Length and Convexity
  10. Parallel Transports
  11. Space Forms
  12. Riemannian Submersions
  13. Lie groups

Sections Taught This Semester:

For more information on instructors and sections for this course, please see our Teaching Schedule Page

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

Phone: +1.848.445.2390
Fax: +1.732.445.5530