Event Type:

Ph.D.Defense

Date/Time:

Tuesday, November 16, 2010 - 07:00 to 09:00

Location:

Weniger 304

Guest Speaker:

Institution:

Oregon State University and Flathead Valley Community College

Abstract:

The degenerate nature of the metric on hypersurfaces creates many difficulties when attempting to define a covariant derivative on the submanifold. This dissertation investigates

these challenges and provides a technique for defining a connection on hypersurfaces in some cases. Recent approaches using decomposition to define a covariant derivative on

hypersurfaces are investigated with examples demonstrating the limitations of the methods. Motivated by Geroch's work on asymptotically flat spacetimes, conformal transformations are used

to construct a covariant derivative on hypersurfaces. In addition, a condition on the Ricci tensor is given to determine when this method is permitted. All of the results are motivated

through a sequence of examples of surfaces on which the covariant derivative is defined. Finally, a covariant derivative operator is given for the class of spherically symmetric

hypersurfaces.

Host: