Math 346 - Differential Geometry II

(See Math 345 - Differential geometry I)

[Top]     [Home]             Instructor: Alex Degtyarev     Office: SA 130     Phone: x2135     Mail: no spam
  • Class syllabus
  • Detailed weekly schedule
  • Topics causing problems
  • Exam rules and terms
  • Class roster

  • Textbook:     Manfredo do Carmo, Differential Geometry of Curves and Surfaces. Prentice-Hall, 1976.
  • Intrinsic geometry of surfaces (continued):
     - review of Math 345;
     - the Gauss-Bonnet theorem;
     - the exponential map;
     - shortest geodesics.
  • Global differential geometry of surfaces:
     - rigidity of the sphere;
     - completeness {\it vs.} geodesic completeness;
     - the Bonnet theorem (compactness of surfaces of positive curvature);
     - Jacobi fields and conjugate points; Jacobi's theorem;
     - Hadamard theorem (on surfaces of negative curvature);
     - surfaces of zero Gaussian curvature;
     - abstract surfaces;
     - Hilbert's theorem on the hyperbolic plane;
     - ... (whatever time permits).

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    Midterm I     (25%)      
    important remarks

    Topics covered (tentative):    
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    Midterm II     (25%)      
    important remarks

    Topics covered (tentative):    
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    Final     (40%)      
    important remarks

    Topics covered* (tentative):    
    All previous material is fully included!
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    Homeworks     (10%)   Approximately weekly
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    During the exams please keep in mind the following:
  • Calculators are  not  allowed
  • Identical solutions (especially identically wrong ones) will  not  get credit. I reserve the right to decide what "identical" means. You still have the right to complain
  • Do not argue about the distribution of the credits among different parts of a problem. I only accept complaints concerning my misunderstanding/misreadung your solution
  • Show all your work. Correct answers without sufficient explanation might  not  get full credit
  • Indicate clearly and unambiguously your final result. In proofs, state explicitly each claim
  • Do not misread the questions or skip parts thereof. If you did, do not complain
  • If you believe that a problem is misstated, do not try to solve it; explain your point of view instead
  • Each problem has a reasonably short solution. If your calculation goes completely out of hands, something must be wrong

    Grading policy
    I will take off a few (2-3) points for arithmetical mistakes. However,  a lot  of points will be taken off for `obvious' mistakes, i.e., either those that you can easily avoid or those showing a deep misunderstanding of the subject.
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