Abstract
We introduce two kinds of covariant derivatives defined on a real hypersurface in Kähler manifolds with respect to the Levi-Civita connection and the $k$-th generalized Tanaka-Webster connection (shortly, gTW-connection). Related to such two kinds of derivatives, we study a generalized parallelism of structure Jacobi operator on a real hypersurface in complex Grassmannians with rank two. And by using this property, we will give some classification results of real hypersurfaces in complex Grassmannians of rank two.
Funding Statement
This work was supported by grant Proj. No.NRF-2022-R1A2C-100456411 from National Research Foundation of the Republic of Korea. The first author was supported by grant Proj. No.NRF-2020R1G1A1A-01003570, the second author by NRF-2022-R1I1A1A-01055993, and the third by NRF-2020R1I1A1A-01067835.
Citation
Gyu Jong KIM. Hyunjin LEE. Eunmi PAK. "Derivatives of structure Jacobi operator on real hypersurfaces in complex Grassmannians of rank two." Hokkaido Math. J. 53 (2) 247 - 283, June 2024. https://doi.org/10.14492/hokmj/2022-656
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