Energy-Momentum tensor on foliations
Differential Geometry
2009-11-13 v1
Abstract
In this paper, we give a new lower bound for the eigenvalues of the Dirac operator on a compact spin manifold. This estimate is motivated by the fact that in its limiting case a skew-symmetric tensor (see Equation \eqref{eq:16}) appears that can be identified geometrically with the O'Neill tensor of a Riemannian flow, carrying a transversal parallel spinor. The Heisenberg group which is a fibration over the torus is an example of this case. Sasakian manifolds are also considered as particular examples of Riemannian flows. Finally, we characterize the 3-dimensional case by a solution of the Dirac equation
Cite
@article{arxiv.0707.0186,
title = {Energy-Momentum tensor on foliations},
author = {Georges Habib},
journal= {arXiv preprint arXiv:0707.0186},
year = {2009}
}