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1 = Riemannian geometry, spring 2016 =
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3
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5 {{panel}}
6 **Teacher:** [[Ilkka Holopainen>>doc:mathstatHenkilokunta.Holopainen, Ilkka]]
7
8 **Scope:** 10 cr
9
10 **Type:** Advanced studies
11
12 **Teaching: **Weeks 3-9 and 11-18, Wednesday 10-12 and Thursday 10-12 in room C123.**
13 **
14
15 **Topics:**
16
17 * Differentiable manifolds (brief review if needed)
18 * Riemannian metrics
19 * Connections
20 * Geodesics
21 * Curvature
22 * Jacobi fields
23 * Curvature and topology
24 * Comparison geometry
25 * The sphere theorem (optional)
26
27 **Prerequisites: **Vector analysis, topology, linear algebra, some knowledge on smooth manifolds
28 (like the course (% class="external-link" %)"[[Introduction to differential geometry>>url:http://wiki.helsinki.fi/display/mathstatKurssit/Introduction+to+differential+geometry%2C+fall+2015||shape="rect"]]"(%%)) and on differential equations.**
29 **
30 {{/panel}}
31
32 === {{toc maxLevel="4" minLevel="2" indent="20px"/}} ===
33
34 == News ==
35
36 *
37
38 == Teaching schedule ==
39
40 Weeks 3-9 and 11-18, Wednesday 10-12 and Thursday 10-12 in room C123.
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42 First lecture on Wednesday, January 20.
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44 Last lecture on Thursday, May 5.
45
46 Easter holiday 24.3.-30.3.
47
48 == Exams ==
49
50 The course can be passed by an (% class="external-link" %)[[exam>>url:https://wiki.helsinki.fi/display/mathstat/General+exams||rel="nofollow" shape="rect"]]. First possibilities are on May 18 or May 24.
51
52 == Course material ==
53
54 * DoCarmo: Riemannian geometry, Birkhäuser, 1992
55 * Lee: Riemannian manifolds, An Introduction to Curvature, Springer, 1997
56
57 Lecture notes (first 101 pages):
58
59 Ilkka Holopainen and Tuomas Sahlsten:  [[Riemannian Geometry>>url:http://wiki.helsinki.fi/download/attachments/58367658/RiemannGeo.pdf||rel="nofollow" shape="rect" class="external-link"]]
60
61 == [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57284||shape="rect"]] ==
62
63
64 (% style="color: rgb(96,96,96);" %)Did you forget to register? (%%)[[What to do?>>url:https://wiki.helsinki.fi/display/mathstatOpiskelu/Kysymys4||style="text-decoration: underline;" shape="rect"]]
65
66 == Exercises ==
67
68 === Assignments and solutions ===
69
70 [[Exercise 1>>attach:rg16h1.pdf]] [[Solutions 1>>attach:rg16ratk1.pdf]]
71
72 [[Exercise 2>>attach:rg16h2.pdf]] [[Solutions 2>>attach:rg16ratk2.pdf]]
73
74 [[Exercise 3>>attach:rg16h3.pdf]] [[Solutions 3>>attach:rg16ratk3.pdf]]
75
76 [[Exercise 4>>attach:rg16h4.pdf]] [[Solutions 4>>attach:rg16ratk4.pdf]]
77
78 [[Exercise 5>>attach:rg16h5.pdf]] [[Solutions 5>>attach:rg16ratk5.pdf]]
79
80 [[Exercise 6>>attach:rg16h6.pdf]] [[Solutions 6>>attach:rg16ratk6.pdf]]
81
82 [[Exercise 7>>attach:rg16h7.pdf]] [[Solutions 7>>attach:rg16ratk7.pdf]]
83
84 [[Exercise 8>>attach:rg16h8.pdf]] [[Solutions 8>>attach:rg16ratk8.pdf]]
85
86 [[Exercise 9>>attach:rg16h9.pdf]] [[Solutions 9>>attach:rg16ratk9.pdf]]
87
88 [[Exercise 10>>attach:rg16h10.pdf]] [[Solutions 10>>attach:rg16ratk10.pdf]]
89
90 [[Exercise 11>>attach:rg16h11.pdf]] [[Solutions 11>>attach:rg16ratk11.pdf]]
91
92 === Exercise classes ===
93
94 |=(((
95 Group
96 )))|=(((
97 Day
98 )))|=(((
99 Time
100 )))|=(((
101 Room
102 )))|=(% colspan="1" %)(((
103 Instructor
104 )))
105 |(((
106 1.
107 )))|(((
108 Tuesday
109 )))|(((
110 12-14
111 )))|(((
112 B321
113 )))|(% colspan="1" %)(((
114 Esko Heinonen
115 )))
116
117 You will get extra credit points by solving the home work exercises:
118
119 25% = +1p, 35% = +2p, 45% = +3p, 55% = +4p, 65% = +5p ja 75% = +6p.
120
121 == Course feedback ==
122
123 Course feedback can be given at any point during the course. Click [[here>>url:https://elomake.helsinki.fi/lomakkeet/11954/lomake.html||style="line-height: 1.4285;" shape="rect"]].