The Energy-Momentum tensor on low dimensional $\Spinc$ manifolds

Abstract

On a compact surface endowed with any $\Spinc$ structure, we give a formula involving the Energy-Momentum tensor in terms of geometric quantities. A new proof of a Bär-type inequality for the eigenvalues of the Dirac operator is given. The round sphere ${\mathbb{S}}^2$ with its canonical $\Spinc$ structure satisfies the limiting case. Finally, we give a spinorial characterization of immersed surfaces in ${\mathbb{S}}^2\times \mathbb{R}$ by solutions of the generalized Killing spinor equation associated with the induced $\Spinc$ structure on ${\mathbb{S}}^2\times \mathbb{R}$

References in corpus (1)

• Energy-Momentum tensor on foliations