Geometric realizations of algebraic curvature models

Peter B. Gilkey. University of Oregon.

Resumo:

In solving certain problems in differential geometry, it is often convenient to work first in a purely algebraic context and then consider subsequent integrability questions, if any, when one passes to the geometric setting. One says R is an algebraic curvature operator if it has the symmetries of the curvature operator of a torsion free connection on the tangent bundle of a smooth manifold or, in a slightly different context, of the curvature tensor of the Levi-Civita connection on a pseudo-Riemannian manifold. We shall examine certain geometric realization questions in these regards. The talk is intended to be a non-technical one and reports on recent work with M. Brozos-Vázquez, H. Kang, S. Nikcevic and G. Weingart

© Peter B. Gilkey.