$\mathfrak A$-principal Hopf hypersurfaces in complex quadrics
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866910294763110400 |
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| author | Loo, Tee-How |
| author_facet | Loo, Tee-How |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1712_00538 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | $\mathfrak A$-principal Hopf hypersurfaces in complex quadrics Loo, Tee-How Differential Geometry 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. |
| title | $\mathfrak A$-principal Hopf hypersurfaces in complex quadrics |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1712.00538 |