SUNY at Stony Brook MAT 568: Differential Geometry
Fall 2024

General Information

Place and time: MW 9:30-10:50am, Physics P122

Professor: Mikhail Movshev

Office: Math Tower 4-109

Office hours: TBA

Course description: This course constitutes the first half of a two-semester introduction to Riemannian geometry. Presupposing only a basic familiarity with manifolds and tensor fields, we will first develop a working knowledge of Riemannian metrics, connections, and curvature. We will then begin our study of the interplay between topology and curvature.

Prerequisite: Geometry/Topology II, a passing grade on the comprehensive exam, or the professor's expressed permission.

Textbooks:

  • Riemannian Geometry,by Manfredo Do Carmo,Birkhäuser, 1992.
  • J. Lee, Riemannian Manifolds: An Introduction to Curvature 1997
  • S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, 3rd ed., 2004
  • Homework and grading: Those who wish to enhance their understanding of the subject are encouraged to complete the homework assignments posted in the syllabus section. Solutions to the problems will be made available at a later time. Once the solutions are posted, please grade your work (assigning a score out of 10 for each problem) and email me your grades. The syllabus will be updated as the semester progresses. Be sure to check this page before starting work on any assignment.

    Exams: There are no exams in this course.

    Information for students with disabilities
    If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact Disability Support Services at (631) 632-6748 or http://studentaffairs.stonybrook.edu/dss/. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

    Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website: http://www.stonybrook.edu/ehs/fire/disabilities.shtml