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Final Exam 2pm, June 8, 2017, Room: 5107 Mid-term Exam covering Lectures 1-9: 7pm, April 15, 2017, Room: 5207 |
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[JJ, Sec. 1.4], [WSY, Chap. 3], [doC, Chap. 3.1-3.3],[PP, Chap. 5.5]
[JJ, Sec. 1.4], [JJ, Sec.1.6]
Lecture 4 Connections, Parallelism, and Covariant Derivatives (I) Lecture 5 Connections, Parallelism, and Covariant Derivatives (II) [doC, Chap. 2], [WSY, Chap. 1 and 2], [Spivak II, Chap. 6]Lecture 6 Connections, Parallelism, and Covariant Derivatives (III) [JJ, Sec.4.1], [doC, Chap. 9.1], Gauss' Lemma [CE, Lemma 1.6], [Spivak I, Chap. 9, Lemma 15] [doC, Chap. 9.2], [JJ, 4.1] [Spivak II, Chap. 4D, Chap. 6, Thm 10], [PP, Chap. 2, Sec. 3] [doC, Chap.9.3],[JJ, Thm 1.5.1], [PP. Chap. 6, Sec. 4], [WSY, Chap. 6]Lecture 11 Space forms and Jacobi fileds (I) [WSY, Chap.4],[XIN, Chap. 8 and 10]Lecture 12 Space forms and Jacobi fileds (II) [WSY, Chap.7],[Spivak IV, Chap.8,1-10]Lecture 13 Space forms and Jacobi fileds (III) [WSY, Chap. 5], [XIN, Chap.9], [Spivak IV, Chap.8, 11-14]Lecture 14 Comparison theorems (I) [Spivak IV, Chap.8, 15-23], [WSY, Chap. 8]Lecture 15 Comparison theorems (II) [Spivak IV, Chap.8, 26-32], [WSY, Chap. 10 and Chap. 8]Lecture 16 Comparison theorems (III) [Spivak IV, Chap.8, 33-36], [WSY, Chap. 8 and Chap. 11]Lecture 17 Candidates for synthetic curvature conditions (I) [JJ, Lemma 4.8.3-Corollary 4.8.5], [JJ2, Chap. 2]Lecture 18 Candidates for synthetic curvature conditions (II) [WSY, Chap. 12]， [WC, Chap. 1] |
Excercises 1 and 2 are due March 9 (Thursday) Excercises 3 and 4 are due March 23 (Thursday) Excercises 5 and 6 are due April 6 (Thursday) Excercise 7 are due April 20 (Thursday) Excercises 8,9,10,11 are due May 04 (Thursday) Excercises 12,13, and 14 are due May 18 (Thursday) |
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[WSY] 伍鸿熙，沈纯理，虞言林，黎曼几何初步，高等教育出版社。 [WC] 伍鸿熙，陈维桓，黎曼几何选讲，北京大学出版社。 [XIN] 忻元龙，黎曼几何讲义，复旦大学出版社。 [JJ] Jürgen Jost, Riemannian geometry and geometric analysis, fifth edition, Universitext, Springer. [JJ2] Jürgen Jost, Nonpositive Curvature: Geometric and Analytic Aspects, Lectures in Mathematics ETH Zürich, Birkhäuser. [doC] M. P. do Carmo, Riemannian geometry, Birkhäuser. [PP] Peter Petersen, Riemannian geometry, GTM 171, Springer. [Spivak I] Michael Spivak, A comprehensive introduction to differential geometry, Volume I, third edition, Publish or Perish. [Spivak II] Michael Spivak, A comprehensive introduction to differential geometry, Volume II, third edition, Publish or Perish. [Spivak IV] Michael Spivak, A comprehensive introduction to differential geometry, Volume IV, third edition, Publish or Perish. [CE] J. Cheeger and E. Ebin, Comparison Theorem in Riemannian geometry, North-Holland Publishing Company, 1975. |
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桂耀挺 vigney@mail.ustc.edu.cn 1. First tutorial: Saturday 7:30 pm-, March 11, 2017, location: 5107 2. 习题课（Tutorial) 7:30- pm, Saturday, March 25, Room 5107. Sol. Excercise 3 (by Yaoting Gui)Sol. Excercise 4 (by Yaoting Gui)Sol. Excercise 5 (by Yaoting Gui)Sol. Excercise 6 (by Yaoting Gui)Sol. Excercise 12,13,and 14 (by Yaoting Gui) |
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1. History about the work of Riemann, Christoffel, Ricci, Levi-Civita, and Einstein 2. A visual introduction to Riemannian curvatures and discrete generalizations by Yann Ollivier, including an interesting pictorial intuition about Bianchi Identity. |