Complex Riemannian Foliations of open K\"ahler manifolds

TL;DR

This paper classifies complex Riemannian foliations on open subsets of irreducible Hermitian symmetric spaces, providing a comprehensive understanding of their structure through curvature analysis and extending results to non-compact symmetric spaces and general K"ahler manifolds.

Contribution

It offers a complete classification of complex Riemannian foliations on certain symmetric spaces using the infinitesimal model and canonical connection, and establishes rigidity results for K"ahler manifolds.

Findings

Complete classification of foliations on compact symmetric spaces

Rigidity results for irreducible K"ahler manifolds

Explicit control over curvature tensors aids classification

Abstract

Classification results for complex Riemannian foliations are obtained. For open subsets of irreducible Hermitian symmetric spaces of compact type, where one has explicit control over the curvature tensor, we completely classify such foliations by studying the infinitesimal model associated to the canonical connection. We also establish results for symmetric spaces of non-compact type and a general rigidity result for any irreducible K\"ahler manifold.