Energy-Momentum tensor on foliations

Georges Habib (1)

1 IECN - Institut Élie Cartan de Nancy

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

Domaines: Géométrie différentielle [math.DG]

Georges Habib. Energy-Momentum tensor on foliations. 2007. ⟨hal-00159103⟩