Cyclic parallel structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians. Issue 4 (August 2022)

• Record Type: Journal Article
• Authors: Lee, Hyunjin; Suh, Young Jin; Woo, Changhwa
• Is Part Of: Proceedings. Volume 152:Issue 4(2022)
• Page Start: 939
• Page End: 964
• Publication Date: 2022-08
• Subjects: Hopf real hypersurface -- complex two-plane Grassmannians -- (quadratic) Killing tensor -- cyclic parallelism -- structure Jacobi operator; 53C40 -- 53C15; Mathematics -- Periodicals; 510
• DOI: 10.1017/prm.2021.42
• Languages: English
• ISSNs: 0308-2105

Abstract

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.