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MATH 346 - DIFFERENTIAL GEOMETRY II
Spring 2000, Spring 2003, Spring 2008, Spring 2010
Math346: Differential Geometry II. A fourth year course.
Text Book : Differential Geometry of Curves and Surfaces, by
Manfredo P. do Carmo. Prentice-Hall, New Jersey , 1976.
Other books :
Barret O'Neill, Elementary Differential Geometry,
Academic Press (second edition)
Differential Geometry ,
Curves
Surfaces1 ,
Surfaces2 ,
symmetry
Content : In this period the remaining last two
chapters of " Manfredo P. do Carmo " will be covered. See the
"Course Syllabus" below
Course Schedule
Monday 8.40-10.30 , SAZ-19
Wednesday 10.40-12.30 , SAZ-19
Exams
(30%) First Midterm Exam pdf file
(2003) ,
(2008) ,, (2010) ,
: March 17. (10.40-12.30) SAZ19 .
(30%) Second Midterm Exam pdf file
(2003) ,
(2008) , (2010)
: April 28. (10.40-12.30) SAZ19 .
(30%) Second Midterm Exam pdf file
(2003) ,
(2008) , (2010)
: April 28. (10.40-12.30) SAZ19 .
Makeup exam (2010)
: May 31, 2010 (10.00-12.00) SAZ18 .
homework and exam grades (2003)
You are responsable from the sections of Chapter 4 which were covered
by Prof. Degtyarev.
I will review the sections 5.1,5.2 and 5.3 which were
also covered by Prof. Degtyarev.
ASSIGNED EXERCISES:
1. Geodesics and Parallel Transport (Section 4.4 of do Carmo).
2. (The Holonomy Group) 1. Exercise 22 in Section 4.4 and
2.Exercise 14 in Section 4.6 (do Carmo)
3. Exponential Mapping (Section 4.6 of do Carmo).
4. Gauss-Weingarten-Codazzi Equations
5. Isometry, Infinitesimal Isomtery and Killing
Vectors
6. Calculus of Variations
Subjects covered
1. February 1
The Rigidity of the Sphere (Chapter 5)
Complete surfaces and Hopf-Rinow Theorem
2. February 8
First and Second Variation of Arc Length
Bonnet`s Theorem
3. February 15
Jacobi Fields and Conjugate points
4. February 22
Jacobi fields
5. March 1
Jacobi Fields
6. March 8
Covering spaces
7. March 15
First Midterm Exam
8. March 22
Covering spaces and Hadamard Theorems
9. March 29
Synge's Lemma
Some global theorems for closed curves
10. April 12
Jordan closed curve theorem
Killing Vector fields
11. April 19
Fenchel and Fary-Milnor theorems
Calculus of variations in Differential Geometry
12. April 26
Fary-Milnor Theorem
Calculus of variations in Differential Geometry
Second Midterm Exam
13. May 3
Calculus on Euclidean Space (Chapter 1 of Peter O'Neil)
14. May 10
Frame Fields (Sections 2.5-2.8, 6.1-6.2 of Peter O'Neil)
Course Syllabus
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