Roger Nakad

Lower bounds for the eigenvalues of the Dirac operator on Spinc manifolds

In this paper, we extend the Hijazi inequality, involving the Energy-Momentum tensor, for the eigenvalues of the Dirac operator on Spin c manifolds without boundary. The limiting case is then studied and an example is given.

The Energy-Momentum tensor on low dimensional Spin c manifolds

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 Bar-type inequality for the eigenvalues of the Dirac operator is given. The round sphere 𝕊2 with its canonical Spinc structure satisfies the limiting case. Finally, we give a spinorial characterization of immersed surfaces in 𝕊2 × ℝ by solutions of the generalized Killing spinor equation associated with the induced Spinc structure on 𝕊2 × ℝ.

Complex and Lagrangian surfaces of the complex projective plane via Kählerian Killing Spinc spinors

Abstract The complex projective space C P 2 of complex dimension 2 has a Spin c structure carrying Kahlerian Killing spinors. The restriction of one of these Kahlerian Killing spinors to a surface M 2 characterizes the isometric immersion of M 2 into C P 2 if the immersion is either Lagrangian or complex.