Holomorphic maps between closed SU(l,m)-orbits in Grassmannian
Complex Variables
2018-09-07 v1
Abstract
Orbits of in a Grassmannian manifold have homogeneous CR structures. In this paper, we study germs of smooth CR mappings sending a closed orbit of into a closed orbit of in Grassmannian manifolds. We show that if the signature difference of the Levi forms of two orbits is not too large, then the mapping can be factored into a simple form and one of the factors extends to a totally geodesic embedding of the ambient Grassmannian into another Grassmannian with respect to the standard metric. As an application, we give a sufficient condition for a smooth CR mapping sending a closed orbit of into a closed orbit of in Grassmannian manifolds to extend as a totally geodesic embedding of the Grassmannian into another Grassmannian.
Cite
@article{arxiv.1809.01933,
title = {Holomorphic maps between closed SU(l,m)-orbits in Grassmannian},
author = {Sung-Yeon Kim},
journal= {arXiv preprint arXiv:1809.01933},
year = {2018}
}