Overview

Description

CALENDAR DESCRIPTION:

Held jointly with MATH 495-3. See description for MATH 495-3. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

COURSE DETAILS:

Differential geometry of curves and surfaces in three-dimensional Euclidan space, first and second fundamental forms, Gauss curvature. Covariant derivative and geodesics. Gauss' Theorema Egregium. Manifolds. Riemannian merics, corrections and geodesics. The curvature tensore. Selected introductory topics in general relativity.

Outline:

• The Local Theory of Curves Tangents, normals and bi-normals, curvature and torsion, Frenet formulas
• The Local Theory of Surfaces Tangent plane, first fundamental form, Gauss map, second fundamental form, curvature of surfaces (normal curvature, Gauss and mean curvatures)
• The Intrinsic Geometry of Surfaces Covariant derivitive, parallel displacement and geodesics, the Gaussian equation and the Theorema Egregium
• Manifolds The notion of a manifold, tangent space, Riemannian metrics, Riemannian connection, tensors, the curvature tensor
• Selected Introductory Topics in General Relativity Gravity as a space time curvature, the geometry of curved space time (geodesics, the field equations), orbits in general relativity, the bending of light.

Grading

Materials

REQUIRED READING: