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$\mathfrak D^\perp$-invariant real hypersurfaces in complex Grassmannians of rank two. (arXiv:1712.04478v1 [math.DG])
来源于:arXiv
Let $M$ be a real hypersurface in complex Grassmannians of rank two. Denote
by $\mathfrak J$ the quaternionic K\"{a}hler structure of the ambient space,
$TM^\perp$ the normal bundle over $M$ and $\mathfrak D^\perp=\mathfrak
JTM^\perp$. The real hypersurface $M$ is said to be $\mathfrak
D^\perp$-invariant if $\mathfrak D^\perp$ is invariant under the shape operator
of $M$. We showed that if $M$ is $\mathfrak D^\perp$-invariant, then $M$ is
Hopf. This improves the results of Berndt and Suh in [{Int. J. Math.}
\textbf{23}(2012) 1250103] and [{Monatsh. Math.} \textbf{127}(1999), 1--14]. We
also classified $\mathfrak D^\perp$ real hypersurface in complex Grassmannians
of rank two with constant principal curvatures. 查看全文>>