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Cyclic parallel structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 4 / August 2022
- Published online by Cambridge University Press:
- 12 August 2021, pp. 939-964
- Print publication:
- August 2022
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- Article
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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.
