Eigenvalues of the transversal Dirac operator on Kahler foliations

TL;DR

This paper establishes inequalities for eigenvalues of the transversal Dirac operator on Kähler foliations, characterizes the limiting cases as minimal Einstein foliations, and introduces transversal Kählerian twistor operators.

Contribution

It introduces transversal Kählerian twistor operators and characterizes limiting cases of Kirchberg inequalities for Kähler spin foliations.

Findings

Kirchberg inequalities are proven for Kähler spin foliations

Limiting cases are characterized as transversal minimal Einstein foliations

Transversal Kählerian twistor operators are introduced

Abstract

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.