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

• Autores: Hyunjin Lee, Eunmi Park, Young Jin Suh
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 117, Nº 2, 2015, págs. 217-230
• Idioma: inglés
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• Resumen

  • 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.