Geometry II

661

An introduction to the differential geometry of curves and surfaces.

Text: 

Topics in Modern Geometry, a coursepak by Saul Stahl.

Prerequisite: 

MATH 660 or permission of instructor.

Credit Hours: 
3

TOPICS:

  1. Surfaces in R : Tangent planes, Gaussian curvature, the First Fundamental Form, Sectional curvatures, Geodesics, Gauss's theorem for geodesic polygons, polyhedral surfaces, intrinsic geometry.
  2. Rudiments of Riemannian geometry: Riemann metrics, geodesics, isometries, curvature.
  3. Non-Euclidean geometry: The geometry of the upper-halfplane, neutral geometry, the half-plane theorem of Pythagoras, isometries of the half-plane.
  4. Topics in spherical geometry and the geometry of complex numbers.

(Stahl 2010 )

Frequency: 
Even Spring Semesters Only

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