# Hypersurfaces in the noncompact Grassmann manifold SU_{2,m}/S(U_2U_m)

## TL;DR

This paper studies hypersurfaces in a complex and quaternionic symmetric space, focusing on how their tangent bundle substructures relate to their shape, advancing understanding of geometric properties in such spaces.

## Contribution

It introduces new insights into the geometric structure of hypersurfaces in SU_{2,m}/S(U_2U_m), especially regarding the interaction of complex and quaternionic subbundles with the hypersurface shape.

## Key findings

- Characterization of hypersurfaces with specific subbundle properties
- Relations between complex and quaternionic structures and hypersurface curvature
- New classifications of hypersurfaces based on subbundle interactions

## Abstract

The Riemannian symmetric space SU_{2,m}/S(U_2U_m) is both Hermitian symmetric and quaternionic Kahler symmetric. Let M be a hypersurface in SU_{2,m}/S(U_2U_m) and denote by TM its tangent bundle. The complex structure of SU_{2,m}/S(U_2U_m) determines a maximal complex subbundle C of TM, and the quaternionic structure of SU_{2,m}/S(U_2U_m) determines a maximal quaternionic subbundle Q of TM. In this article we investigate hypersurfaces in SU_{2,m}/S(U_2U_m) for which C and Q are closely related to the shape of M.