Structure des feuilletages k\"ahleriens en courbure semi-n\'egative

TL;DR

This paper investigates the structure of transversally Kähler foliations under semi-negative curvature conditions, showing that the Lie algebra of the holonomy pseudo-group is semi-simple when the Ricci tensor is non-positive.

Contribution

It establishes a new link between semi-negative Ricci curvature and the semi-simplicity of the holonomy Lie algebra in Kähler foliations.

Findings

Holonomy Lie algebra is semi-simple under semi-negative Ricci curvature.

Provides structural insights into transversally Kähler foliations.

Extends understanding of curvature conditions in foliated geometry.

Abstract

This paper is concerned with (transversally) K\"ahler foliations. We proved here that the holonomy pseudo-group's lie algebra is semi-simple unde negativity assumptions of the Ricci tensor.