Complex Riemannian Foliations of open K\"ahler manifolds
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.
Keywords
Cite
@article{arxiv.1512.04390,
title = {Complex Riemannian Foliations of open K\"ahler manifolds},
author = {Thomas Murphy and Paul-Andi Nagy},
journal= {arXiv preprint arXiv:1512.04390},
year = {2019}
}
Comments
V3: Added Publication details. Manuscript differs very slightly from published version as a typographical error in line 3 of Table 1 (of V2) is corrected. This means that one of the cases ruled out in Table 2 (of V2) does not need to be considered. Consequently lines 14--16 of page 15 (of V2) were slightly modified to take this into account. The rest of the paper is unaffected