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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