The first eigenvalue of the Dirac operator in a conformal class

Bernd Ammann (1) , Emmanuel Humbert (1)

1 IECN - Institut Élie Cartan de Nancy

In this overview article, we study the first positive eigenvalue of the Dirac operator in a unit volume conformal class. In particular, we discuss the question whether the infimum is attained. In the first part, we explain the corresponding variational problem. In the following parts we discuss the relation to the spinorial mass endomorphism and an application to surfaces of constant mean curvature. The article also mentions some open problems and work in progress.

Domaines: Géométrie différentielle [math.DG]

Bernd Ammann, Emmanuel Humbert. The first eigenvalue of the Dirac operator in a conformal class. Symmetry in Geometry and Physics, conference in Honour of D. V. Alekseevsky, 2005, Rome, Italy. ⟨hal-00098394⟩