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

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

2012-04-02

arxiv.org/abs/1204.0541v1

Mathematics

Differential Geometry

Scientific paper

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 B\"{a}r-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 $\mathbb{S}^2\times \mathbb{R}$

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