Derivatives of structure Jacobi operator on real hypersurfaces in complex Grassmannians of rank two (Q6566514)

\textit{J. T. Cho} [Publ. Math. Debr. 54, No. 3--4, 473--487 (1999; Zbl 0929.53029)] introduced the \(k\)-th generalized Tanaka-Webster connection on any real hypersurface of a Kähler manifold, which generalizes the well-known connection due to \textit{S. Tanno} [Trans. Am. Math. Soc. 314, No. 1, 349--379 (1989; Zbl 0677.53043)].\N\NIn the present paper, the authors introduce two kinds of covariant derivatives defined on a real hypersurface of a Kähler manifold with respect to the Levi-Civita connection and the \(k\)-th generalized Tanaka-Webster connection. Related to these two kinds of derivatives, they investigate a generalized parallelism of structure Jacobi operator on a real hypersurface in complex Grassmannians of rank two. The authors also present some classification results for real hypersurfaces in complex Grassmannians of rank two.