Revista de la
Unión Matemática Argentina
The $\mathfrak{A}$-principal real hypersurfaces in complex quadrics
Tee-How Loo
Volume 63, no. 1 (2022), pp. 69–91

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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 $Q^m$. The classification for complete pseudo-Einstein real hypersurfaces in $Q^m$, $m\geq3$, is also obtained.