Eigenvalues of the transversal Dirac operator on Kahler foliations

Georges Habib (1)

1 IECN - Institut Élie Cartan de Nancy

In this paper, we prove Kirchberg inequalities for any kahler spin foliations. Their limiting cases are then characterized as being transversal minimal Einstein foliations. The key point is to introduce the transversal kahlerian twistor operators.

Mots clés: Kahler foliations; transversal Dirac operator; eigenvalues

Domaines: Géométrie différentielle [math.DG]

Georges Habib. Eigenvalues of the transversal Dirac operator on Kahler foliations. Journal of Geometry and Physics, 2006, 56, pp.260-270. ⟨hal-00159109⟩