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

Georges Habib (1) , Roger Nakad (2)

1 LU / ULB - الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth]
2 MPIM - Max Planck Institute for Mathematics

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 $\mathbb{S}^2\times \mathbb{R}$

Domaines: Géométrie différentielle [math.DG]

Georges Habib, Roger Nakad. The Energy-Momentum tensor on low dimensional $\Spinc$ manifolds. 2012. ⟨hal-00684703⟩