## MATH 434 - DIFFERENTIAL GEOMETRY II

## Spring 2000:

**Math434: 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.

** Content **: In this period the remaining last two
chapters of " do Carmo " will be covered. See the
"Course Syllabus" below

** Other Books **: ** 1.** A Treatise on the Differential Geometry of
Curves and Surfaces, by ** Luther Pfahler Eisenhart ** , Dover publications ,
New York , 1960.
**2. **Elementary Differential Geometry, by ** Barrett O'Neil**,
Academic Press, Second Edition, 1997.

## Course Schedule

Monday 13.40-15.30 , SBZ-11
Wednsday 13.40-15.30 , SBZ-11

## Exams

** (20%) ** First Midterm Exam: ** March 06** .
** (20%) ** Second Midterm Exam: ** April 03 ** .
** (20%) ** Third Midterm Exam: ** May 15** .
** (30%) ** Final Exam : ** May 24 **.
** (10%) ** For homeworks and attendance.

## Course Syllabus

1. Feb.07- Isometries, conformal maps.

2. Feb.14- Equations of Compatibility.

3. Feb.21- Parallel transport, geodesics.

4. Feb.28- The Gauss-Bonnet Theorem.

5. Mar.06- The exponential Map. ** (M.Ex.1)**

6. Mar.13- Further properties of geodesics.

7. Mar.20- The rigidity of the sphere.

8. Mar.27- Complete surfaces.

9. Apr.03- First and second variations of the arc length. ** (M.Ex.2) **

10. Apr.10- Jacobi fields and conjugate points.

11. Apr.17- Covering spaces.

12. Apr.24- Global theorems on curves.

13. May.01- Surfaces of zero Gaussian curvature. ** (M.Ex.3) **

14. May.08- Abstract surfaces and Hilbert theorem.

15. May.15-Review and Problems

.
## Students

Ali Ekber Gurel

Hali Ugur Ozcevik

Hilal Simsek

Hakan Tasci

## Students of the year 1998-1999

95019370 Han Nazmi Özsöylev
94010000 Burhan Biner
94001560 Yasin Özcelik
94016690 Umud Devrim Yalcin
95020020 Nuray Tugrul
94018050 Pelin Pasin
94030070 Bekir Arslan
95021940 Caner Kazanci
95014330 Bayram Yenikaya
95014300 Aytek Naci Erdil

For exercises please see exercises

For midterms please see midterms

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