Geodesic
Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 569-577.

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We study classifying problems of real hypersurfaces in a complex two-plane Grassmannian $G_2({\mathbb C}^{m+2})$. In relation to the generalized Tanaka-Webster connection, we consider that the generalized Tanaka-Webster derivative of the normal Jacobi operator coincides with the covariant derivative. In this case, we prove complete classifications for real hypersurfaces in $G_2({\mathbb C}^{m+2})$ satisfying such conditions.
DOI : 10.1007/s10587-015-0196-z
Classification : 53B05, 53C15, 53C40
Keywords: real hypersurface; complex two-plane Grassmannian; Hopf hypersurface; Levi-Civita connection; generalized Tanaka-Webster connection; normal Jacobi operator 
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     title = {Generalized {Tanaka-Webster} and {Levi-Civita} connections for normal {Jacobi} operator in complex two-plane {Grassmannians}},
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Pak, Eunmi; Pérez, Juan de Dios; Suh, Young Jin. Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 569-577. doi : 10.1007/s10587-015-0196-z. http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0196-z/

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