$$\mathfrak D $$ -parallelism of normal and structure Jacobi operators for hypersurfaces in complex two-plane Grassmannians
2012; Springer Science+Business Media; Volume: 193; Issue: 2 Linguagem: Inglês
10.1007/s10231-012-0292-8
ISSN1618-1891
AutoresCarlos J. G. Machado, Juan de Dios Pérez, Imsoon Jeong, Young Jin Suh,
Tópico(s)Nonlinear Waves and Solitons
ResumoIn this paper, we give non-existence theorems for Hopf hypersurfaces in complex two-plane Grassmannians $$G_2(\mathbb{C }^{m+2})$$ with $$\mathfrak D $$ -parallel normal Jacobi operator $${\bar{R}}_N$$ and $$\mathfrak D $$ -parallel structure Jacobi operator $$R_{\xi }$$ if the distribution $$\mathfrak D $$ or $$\mathfrak D ^{\bot }$$ component of the Reeb vector field is invariant by the shape operator, respectively.
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