Riemannian Geometry - MATH 537 001, Fall 2025
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Time: 8:30 - 9:45, Location:
Instructor: Dimiter Vassilev, Professor; Office: SMLC, Office 326; Email: vassilev@unm.edu
Office Hours: MW 1:30pm - 2:30pm. Feel free to stop-by anytime if you have a quick question.
Catalog Description: Theory of connections, curvature, Riemannian metrics, Hopf-Rinow theorem, geodesics. Riemannian submanifolds. Prerequisite: 536.
Texts:
1. John M. Lee, Introduction to Riemannian Manifolds (2018), (free access through Springer on the UNM network);
2. Köhler, K. (2024). Differential Geometry and Homogeneous Spaces. Universitext. Springer, (free access through Springer on the UNM network);
3. Sylvestre Gallot , Dominique Hulin, Jacques Lafontaine, Riemannian Geometry (2004);
4. Manfredo P. do Carmo, Riemannian Geometry (1992).
A note on Course Materials Access (the following is a required UNM information only, see also https://coursematerialsaccess.unm.edu/#Complete): Your digital course materials are directly available now on the My Shelf link in Canvas. Your physical course materials, such as books and required lab/studio course kits, are available at the UNM Bookstore, and you will receive an email about how to pick them up. To simplify your course materials access, you are automatically enrolled in a Complete option at a flat rate of $279 per semester. This will show up on your bursar bill. The Complete option covers all your required course materials for all your Albuquerque campus courses, including any graduate courses you may be taking (branch campus course materials are billed and available separately). If you are interested in course materials access for only selected courses, or if you want to opt out entirely, you will need to select the option you want in the My Shelf link in Canvas. You can change your selected option in the My Shelf link in Canvas until the registrar’s “Last Day to Drop Without a ‘W’ Grade and 100% Tuition Refund.” Make sure that you review the video and information here to understand cost and the options for Complete (automatic enrollment), Select (take action), and Opt-out (take action).
Accommodations: UNM is committed to providing equitable access to learning opportunities for students with documented disabilities. As your instructor, it is my objective to facilitate an inclusive classroom setting, in which students have full access and opportunity to participate. To engage in a confidential conversation about the process for requesting reasonable accommodations for this class and/or program, please contact Accessibility Resource Center at arcsrvs@unm.edu or 505-277-3506.
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Credit-hour statement: This is a three-credit-hour course. Class meets for two 75-minute sessions of direct instruction for fifteen weeks during the Fall 2025 semester. Please plan for a minimum of six hours of out-of-class work (or homework, study, assignment completion, and class preparation) each week.
ATTENDANCE: Attendance at UNM is mandatory, see policy.
Topics (can be modified depending on the class interests; don't be shy about asking ASAP to cover a particular topic that is of interest to you and is not listed below)