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Cyclic parallel structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians

Published online by Cambridge University Press:  12 August 2021

Hyunjin Lee
Affiliation:
The Research Institute of Real and Complex Manifolds (RIRCM), Kyungpook National University, Daegu 41566, Repulic of Korea ([email protected])
Young Jin Suh
Affiliation:
Department of Mathematics & RIRCM, Kyungpook National University, Daegu 41566, Repulic of Korea ([email protected])
Changhwa Woo
Affiliation:
Department of Applied Mathematics, Pukyong National University, Busan 48513, Republic of Korea ([email protected])

Abstract

In this paper, from the property of Killing for structure Jacobi tensor $\mathbb {R}_{\xi }$, we introduce a new notion of cyclic parallelism of structure Jacobi operator$R_{\xi }$ on real hypersurfaces in the complex two-plane Grassmannians. By virtue of geodesic curves, we can give the equivalent relation between cyclic parallelism of $R_{\xi }$ and Killing property of $\mathbb {R}_{\xi }$. Then, we classify all Hopf real hypersurfaces with cyclic parallel structure Jacobi operator in complex two-plane Grassmannians.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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