Year: 2012
Type: preprint
Abstract: Motivated by Gray's work on tube formulae for complex submanifolds of complex projective space equipped with the Fubini-Study metric, Riemannian foliations of projective space are studied. We prove that there are no complex Riemannian foliations of any open subset of $\mathbb{P}^n$ of codimension one. As a consequence there is no Riemannian foliation of the projective plane by Riemann surfaces, even locally. We determine how a complex submanifold may arise as an exceptional leaf of a non-trivial singular Riemannian foliation of maximal dimension. Gray's tube formula is applied to obtain a volume bound for certain holomorphic curves of complex quadrics.
Source: arXiv (Cornell University)
Author: Murphy, Thomas
Institution: Université Libre de Bruxelles
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1491483753