Event Detail

Event Type: 
Ph.D.Defense
Date/Time: 
Tuesday, November 16, 2010 - 07:00 to 09:00
Location: 
Weniger 304

Speaker Info

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.