Differenital Geometry and Relativity Theory

MTH

358

Differenital Geometry and Relativity Theory

This course is designed to introduce students in the Space Science P, the Physics Program, and the Mathematical Sciences Program to the application of the differential geometry of curves and surfaces to the classical theory of relativity. The concepts to be discussed will be presented first from a mathematical point of view and then from a physical point of view using mathematical formalism. The topics to be presented will include the theory of space curves and three-dimensional surfaces and their proprieties. These basic differential geometric concepts will then be used to develop the geometric principles that govern flat space-time or the special of relativity. The mathematical topics to be presented in this course will include a brief review of vector geometry and analysis, the hyperbolic functions, the geometry of curves and their representations, the geometry of surfaces in E3, the first fundamental form, the second fundamental form, mean curvature, Gauss curvature, geodesics, the curvature tensor, the Glorious Theorem Gauss and invariance, and extensions and manifolds. The topics from physic to be presented include an informal historical analysis

Fall, Spring

Undergraduate

No

019885