{"id":3065,"date":"2015-08-18T18:27:22","date_gmt":"2015-08-18T22:27:22","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/groisser\/?page_id=3065"},"modified":"2026-03-19T08:12:54","modified_gmt":"2026-03-19T12:12:54","slug":"syllabus","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/groisser\/classes\/6932_and_4930_f15\/syllabus\/","title":{"rendered":"Syllabus and course information"},"content":{"rendered":"\r\n
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Syllabus and course information<\/h1>\n\n\n\n


\nMWF 8th period, LIT 233<\/h3>\n\n\n\n

Link to class home page <\/a><\/p>\n\n\n\n

<\/a> Instructor: <\/b><\/span> David Groisser <\/a><\/p>\n\n\n\n\n\n\n\n\n\n\n\n


\n Office Hours: <\/b><\/font> <\/a> Tentatively Monday 5th period (11:45-12:35) and Wednesday & Friday 9th period (4:05-4:55). Please come early in the period or let me know to expect you later; otherwise I may not stay in my office for the whole period. See my schedule<\/a> for updates. Students who can’t make scheduled office hours may see me by appointment on most weekdays.
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Prerequisite:<\/b><\/span> <\/a> A year of differential geometry at the level of MTG 6256-6257.<\/p>\n\n\n\n\n\n

Textbook:<\/b><\/span> <\/a> None required. However, there are two that I’ll recommend, both of which area available online from the UF library:<\/p>\n\n\n\n

  1. Isaac Chavel, Riemannian Geometry: A Modern Introduction, <\/i> 2nd edition, Cambridge University Press (2006).<\/li>\n

    If you access Chavel’s book online through the UF library, you may reach a page that, for some reason, lists the publication-date as April 2002. You’ve reached the correct book. Inside, the publication-date is stated to be 2006.<\/p>\n

  2. Peter Petersen, Riemannian Geometry,<\/i> 2nd edition, Springer (2006).<\/li>\n

    Note that that’s “Petersen” with an e<\/i>, not “Peterson” with an o<\/i>.<\/p><\/ol>\n\n\n\n

    I will probably draw material (and possibly exercises) from both of these books, as well as other sources. (The material in this course exists in non-textbooks that I’m much more familiar with.) Petersen takes longer than I’d like to get to geodesics; Chavel gets there more quickly than I’d like. Chavel’s notation is closer to mine than Petersen’s, but neither author’s notation is identical to mine. <\/p>\n\n\n\n\n\n

    Syllabus (course content):<\/b><\/span><\/a> This course is intended to be the first semester of a two-semester sequence. I plan to spend most of the fall semester on various topics in Riemannian geometry, including curvature, geodesics, Riemannian manifolds as metric spaces, the Hopf-Rinow Theorem, parallel transport, and some curvature-based comparison theorems (including theorems relating curvature-bounds to global topology). Possible additional topics include applications to Lie groups and homogeneous spaces; submanifolds and the second fundamental form; Riemannian submersions; cut locus; the structure of convex sets.<\/p>\n\n\n\n\n\n

    For a list of some possible topics for the spring semester, click here<\/a>.<\/p>\n\n\n\n\n\n

    Exams, Homework, and Grading: <\/b><\/span> <\/a> There will be no exams. Homework will include some required hand-in problems, and some optional problems for students who want to explore further. I will also expect students to study their notes to keep up with the lectures. Grades will be based on homework and attendance. The workload needed to receive an A will not be burdensome; however, your attendance will need to be good.<\/p>\n\n\n\n\n\n

    Attendance:<\/b><\/span><\/a> I work hard to prepare my lectures, and I expect all enrolled students to attend all of them<\/b>, with the usual allowances for illness, emergency, etc. When you must miss a class, please obtain notes from a classmate. <\/p>\n\n\n\n\n\n

    Student Honor Code. <\/b> <\/span><\/a> UF students are bound by The Honor Pledge, which states:<\/p>\n\n\n\n