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Instructor: Igor Belegradek
office hours: TBA
office: Skiles 240B
phone: (404) 385-0053 (Please do not leave messages).
email: ib at math dot gatech dot edu
(this is the best way to contact me.
Please include 6455 in the subject header).
Course homepage: www.math.gatech.edu/~ib/6455.html
Lectures: TR 9:35 - 10:55 in Architecture (West) 258.
Textbook: The textbook will be Riemannian Geometry, by Manfredo do Carmo, availalable for example at amazon. The text will be supplemented by class notes.
Content and objectives: This course aims to give you firm foundation of higher-dimensional Riemannian geometry, including basic topics such as exponential maps, parallel, curvature, geodesics, and Jacobi fields. There will be digressions depending on students' interests and instructor's whims. The plan is to cover items 1-6 on the official syllabus. No applications outside of mathematics will be covered, yet to some extent the teaching will be informed by students' interests.
Prerequisites: Math 4441 or Math 6452 or permission of the instructor. You need sufficient mathematical maturity to tell correct reasoning from faulty one. It would help to know basics of smooth manifolds, topology and Lie group theory, but these topics reviewed on the go, and in particular, the course will start from a review smooth manifolds.
Grading: Class participation will count for 5%. Essay will count for 15%. Homework will count for 80%. Grades will be kept in T-square. Grading scheme: A=80%, B=60%, C=50%, D=40%.
Homework will be (usually) assigned biweekly and collected in the beginning of the lecture. Late homework will not be accepted unless in emergency, or other unusual situation. You may discuss homework with others and work in groups, but you must write up and submit your own solutions.
Class participation grade will be based on regular attendence, thoughtful questions and comments, and corrections to lecture and notes.
Essay will be an in depth discussion of a particular Riemannian Geometry topic from the list suggested by the instructor. Details on essay requirements will be distributed later but it will be 3-5 pages long (typed), and there will be separate deadlines for the first draft and the final version. I will comment on the former, and grade the latter.