This is an introductory graduate course on Riemannian manifolds. We shall cover Chapters 0-9 of do Carmo, Riemannian Geometry, with some omissions and some supplementary material (e.g., Cartan structure equations).
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Instructor: |
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TA: |
Chenyun Luo |
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Time: |
TuTh 10:30-11:45 |
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Classroom: |
Maryland 202 |
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Text: |
M. P. do Carmo,
Riemannian Geometry, 1992 |
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Supplementary references: |
J.
Lee, Riemannian Geometry, 1997 S.
Gallot, D. Hulin, J.
Lafontaine, Riemannian Geometry,
3rd ed., 2004 |
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Prerequisite: |
Undergraduate
analysis and linear algebra. Some knowledge of topology is recommended. |
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Grading: |
There
will be weekly problem sets and no exams. |
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Syllabus: |
The
syllabus will be updated as the semester progresses. Be sure to check this
page before starting work on any assignment. |
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week |
beginning |
reading |
assignment
(due the following Tuesday) |
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1 |
Thu. Sep. 1 |
Ch. 0, Sec. 1-2 |
(no assignment) |
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2 |
Sep. 6 |
Ch. 0, Sec. 3-5 |
Ch. 0: 1, 2, 5, 9ac, 12ab |
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3 |
Sep. 13 |
Ch. 1 |
Ch. 0: 7, 11. Ch. 1: 2, 3, 4, 6 |
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4 |
Sep. 20 |
Ch. 2, Lee,
pp. 11-21 |
Ch. 2: 1, 2, 3 |
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5 |
Sep. 27 |
Ch. 3, Sec. 1-2 |
Ch. 1: 7. Ch. 2: 4,
7, 8 Ch. 3: 1, 2 |
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6 |
Oct. 4 |
Ch. 3, Sec. 3-4 |
Gallot: 1.118a. Ch. 3: 3a, 4, 5 |
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7 |
Oct. 11 |
Ch. 4, Sec. 1-3 |
Ch. 4: 4, 5, 7 |
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8 |
Oct. 18 |
Ch. 4, Sec. 4-5 |
No
class Oct. 20 (Fall Break) |
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Oct. 25 |
no class this week |
Ch. 3: 7. Ch. 4: 8, 10 |
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9 |
Nov. 1 |
Ch. 5 |
Ch. 5: 1, 3, 6, 7 |
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10 |
Nov. 8 |
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(no assignment) |
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11 |
Nov. 15 |
Ch. 6, Sec. 1-2 |
Ch. 6: 3, 5, 6, 7 |
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Nov. 22 |
Thanksgiving
break |
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12 |
Nov. 29 |
Ch. 7 |
Ch.
7: 5, 6, 9, 10, 12 |
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13 |
Dec. 6 |
Ch. 8: Sec. 3 |
Gallot: 2.11ac. Ch. 9: 1, 3 (due
Dec. 14) |
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14 |
Mon, Dec. 12 |
Ch. 9 |
Class
meetings: Dec. 12 &14, 1:00-2:15 (Gilman 217) |
Last updated
12/8/2016