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Lie Derivatives and Ricci Tensor on Real Hypersurfaces in Complex Two-plane Grassmannians

Published online by Cambridge University Press:  20 November 2018

Imsoon Jeong ,
Juan de Dios Pérez ,
Young Jin Suh  and
Changhwa Woo
Imsoon Jeong
Affiliation:
Division of Future Capability Education, Ju Si-Gyeong College, Pai Chai University, 155-40 Baejae-ro, Seo-gu, Daejeon, 35345, Republic of Korea, e-mail : imsoon.jeong@gmail.com
Juan de Dios Pérez
Affiliation:
Departamento de Geometria y Topologia, Universidad de Granada, 18071-Granada, Spain, e-mail : jdperez@ugr.es
Young Jin Suh
Affiliation:
Department of Mathematics and Research Institute of Real and Complex Manifold, Kyungpook National University, Daegu 41566, Republic of Korea, e-mail : yjsuh@knu.ac.kr
Changhwa Woo
Affiliation:
Department of Mathematics Education, Woosuk University, 565-701 Wanju, Jeonbuk, Republic Of Korea, e-mail : legalgwch@naver.com
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Abstract

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On a real hypersurface $M$ in a complex two-plane Grassmannian ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$ we have the Lie derivation $\mathcal{L}$ and a differential operator of order one associated with the generalized Tanaka–Webster connection ${{\widehat{\mathcal{L}}}^{\left( k \right)}}$. We give a classification of real hypersurfaces $M$ on ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$ satisfying $\widehat{\mathcal{L}}_{\xi }^{\left( k \right)}\,S\,=\,{{\mathcal{L}}_{\xi }}S$, where $\xi$ is the Reeb vector field on $M$ and $s$ the Ricci tensor of $M$.

Keywords

53C4053C15real hypersurfacecomplex two-plane GrassmannianHopf hypersurfaceshape operatorRicci tensorLie derivation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 3 , 01 September 2018 , pp. 543 - 552
Copyright
Copyright © Canadian Mathematical Society 2018

References

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