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Hopf Hypersurfaces in Complex Two-Plane Grassmannians With $\mathfrak{D}$-Parallel Shape Operator

Hyunjin Lee, Eunmi Pak, Young Jin Suh

Abstract


In this paper we consider a generalized condition for shape operator of a real hypersurface $M$ in complex two-plane Grassmannian $G_2(\mathsf{C}^{m+2})$, namely, $\mathfrak{D}$-parallel shape operator of $M$. Using such a notion, we prove that there does not exist a real hypersurface in complex two-plane Grassmannian $G_2(\mathsf{C}^{m+2})$ with $\mathfrak{D}$-parallel shape operator.

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DOI: http://dx.doi.org/10.7146/math.scand.a-22868

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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