Structure of K\"ahler foliations with negative transverse Ricci curvature

TL;DR

This paper studies the geometric structure of Kähler foliations with negative transverse Ricci curvature, providing a decomposition theorem for their leaf spaces and characterizing each component.

Contribution

It introduces a de Rham type decomposition theorem for transversely Kähler foliations with quasi-negative transverse Ricci curvature, advancing understanding of their geometric structure.

Findings

Decomposition theorem for leaf spaces of such foliations

Characterization of each factor in the decomposition

Insights into the structure of negatively curved Kähler foliations

Abstract

We investigate the structure of transversely K\"ahler foliations with quasi-negative tranverse Ricci curvature. In particular, we prove a de Rham type theorem decomposition on the leaf space where we characterize each factor.