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Real Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Structure Jacobi Operator

Published online by Cambridge University Press:  20 November 2018

Imsoon Jeong ,
Seonhui Kim  and
Young Jin Suh
Imsoon Jeong
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu, 702-701, KOREA e-mail: [email protected]@[email protected]
Seonhui Kim
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu, 702-701, KOREA e-mail: [email protected]@[email protected]
Young Jin Suh
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu, 702-701, KOREA e-mail: [email protected]@[email protected]
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Abstract

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In this paper we give a characterization of a real hypersurface of Type $\left( A \right)$ in complex two-plane Grassmannians ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$, which means a tube over a totally geodesic ${{G}_{2}}\left( {{\mathbb{C}}^{m+1}} \right)$ in ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$, by means of the Reeb parallel structure Jacobi operator ${{\nabla }_{\xi }}{{R}_{\xi }}\,=\,0$.

Keywords

53C4053C15real hypersurfacescomplex two-plane GrassmanniansHopf hypersurfaceReeb parallelstructure Jacobi operator
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 4 , 01 December 2014 , pp. 821 - 833
Copyright
Copyright © Canadian Mathematical Society 2014

References

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