Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2017
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/1712.00538 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- A real hypersurface in the complex quadric $Q^m=SO_{m+2}/SO_mSO_2$ is said to be $\mathfrak A$-principal if its unit normal vector field is singular of type $\mathfrak A$-principal everywhere. In this paper, we show that a $\mathfrak A$-principal Hopf hypersurface in $Q^m$, $m\geq3$ is an open part of a tube around a totally geodesic $Q^{m+1}$ in $Q^m$. We also show that such real hypersurfaces are the only contact real hypersurfaces in $Q^m$. %, this answers affirmatively a question posted by Berndt (cf. \cite{berndt1})}. The classification for pseudo-Einstein real hypersurfaces in $Q^m$, $m\geq3$, is also obtained.