Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition. II

Title:

Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition. II

Creator:

Lee, Hyunjin, Kim, Seonhui, and Suh, Young Jin

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:2e3859d8-db0c-4bb1-82c7-0450d9d17731
uuid:2e3859d8-db0c-4bb1-82c7-0450d9d17731

Subject:

complex two-plane Grassmannians, Hopf hypersurface, $\mathfrak D^{\bot }$-invariant hypersurface, commuting shape operator, and Reeb vector field

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Lee, Kim and Suh (2012) gave a characterization for real hypersurfaces $M$ of Type ${\rm (A)}$ in complex two plane Grassmannians $G_2({\mathbb C}^{m+2})$ with a commuting condition between the shape operator $A$ and the structure tensors $\phi $ and $\phi _{1}$ for $M$ in $G_2({\mathbb C}^{m+2})$. Motivated by this geometrical notion, in this paper we consider a new commuting condition in relation to the shape operator $A$ and a new operator $\phi \phi _{1}$ induced by two structure tensors $\phi $ and $\phi _{1}$. That is, this commuting shape operator is given by $\phi \phi _{1} A = A \phi \phi _{1}$. Using this condition, we prove that $M$ is locally congruent to a tube of radius $r$ over a totally geodesic $G_2({\mathbb C}^{m+1})$ in $G_2({\mathbb C}^{m+2})$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

133-148

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:1

Harvested from:

CDK

Metadata only:

false