Real hypersurfaces in complex projective space whose structure Jacobi operator is Lie \(\xi\)-parallel
It is well-known that on any real hypersurface \(M\) of the complex projective space \(\mathbb CP^m\), an almost contact metric structure \((\varphi,\xi,\eta,g)\) is induced. In this paper, it is proved for \(M\) that if \(\mathcal L_{\xi}R_{\xi}=0\), where \(\mathcal L_{\xi}\) is the Lie derivative and \(R_{\xi}\) is the Jacobi operator corresponding to \(\xi\), then \(M\) is locally congruent to a tube of radius \(\pi/4\) over a complex submanifold, or to either a geodesic hypersphere or a tube over totally geodesic \(\mathbb CP^k\), \(0<k<m-1\), with radius \(r\not=\pi/4\). The paper should be compared to the previous one [Publ. Math. 66, No. 3--4, 269--282 (2005; Zbl 1081.53051)].
scientific article; zbMATH DE number 2165116