Exercises Riemannian Geometry (MRI, Mastermath)

See also: theory

Fall semester 2008

(01) Week 36, sep 10

no exercise class this week

(02) Week 38, sep 17

no exercise class this week

(03) Week 39, sep 24

start of exercise class: 16:00 - 17:00.

exercises: Lecture Notes 3.8*; 3.9; 4.2. (* means: to be handed in for grading).

(04) Week 40, oct 1

exercises: Lecture Notes 4.9, 4.20, 7.10*. The latter exercise was originally numbered 5.10. I discovered that the original version was too difficult to do without some extra material. This material will be discussed in class on October 8. The starred exercise will be moved to next week. Note that extra sections 5,6 have been added to the lecture notes.

(05) Week 41, oct 8

Exercise 7.10* (again, with lots of hints).

Exercises 7.7, 7.8.

(06) Week 42, oct 15

Exercises: 13.1*, 13.2.

(07) Week 43, oct 22

Exercises: 13.3, 13.4*, 13.9.

Hint for exercise 3,4: use the geodesic to obtain a limit point p in M. Then apply the Gauss lemma for polar coordinates at p to conclude that the geodesic must have a special form.

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(08) Week 44, oct 29

Last exercise class by Erik van den Ban

Exercises: 13.5*, 13.7, 13.10.

In exercise 13.5 (c), read $d_a = \dim \ker (d\sigma(a) - I).$

(09) Week 45, nov 5

(10) Week 46, nov 12

(11) Week 47, nov 19

(12) Week 48, nov 26

(13) Week 49, dec 3

(14) Week 50, dec 10

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