Real hypersurfaces with Killing type structure Jacobi operators in \(\mathbb{C}P^2\) and \(\mathbb{C}H^2\). (English) Zbl 1401.53016

Wang, Yaning; Wang, Wenjie

Bull. Belg. Math. Soc. - Simon Stevin 25, No. 3, 403-414 (2018).

Summary: In this paper, we prove that if the structure Jacobi operator of a \(3\)-dimensional real hypersurface in a nonflat complex plane is of Killing type, then the hypersurface is either a tube of radius \(\frac{\pi}{4}\) over a holomorphic curve in \(\mathbb{C}P^2\) or a Hopf hypersurface with vanishing Hopf principal curvature in \(\mathbb{C}H^2\). This extends the corresponding results in [T. A. Ivey and P. J. Ryan, Result. Math. 56, No. 1–4, 473–488 (2009; Zbl 1186.53067)].

MSC:

53B25	Local submanifolds
53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
53D15	Almost contact and almost symplectic manifolds

Keywords:

3-dimensional real hypersurface; structure Jacobi operator; Hopf hypersurface; Killing tensor

Citations:

Zbl 1186.53067