Geodesic
Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 3, pp. 849-861.

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In this paper, first we introduce a new notion of commuting condition that ϕϕ1A=Aϕ1ϕ between the shape operator A and the structure tensors ϕ and ϕ1 for real hypersurfaces in G2(Cm+2). Suprisingly, real hypersurfaces of type (A), that is, a tube over a totally geodesic G2(Cm+1) in complex two plane Grassmannians G2(Cm+2) satisfy this commuting condition. Next we consider a complete classification of Hopf hypersurfaces in G2(Cm+2) satisfying the commuting condition. Finally we get a characterization of Type (A) in terms of such commuting condition ϕϕ1A=Aϕ1ϕ.
DOI : 10.1007/s10587-012-0049-y
Classification : 11R52, 53C40, 53C50, 53C55
Mots-clés : real hypersurface; complex two-plane Grassmannians; Hopf hypersurface; commuting shape operator 
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     title = {Real hypersurfaces in complex two-plane {Grassmannians} with certain commuting condition},
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Lee, Hyunjin; Kim, Seonhui; Suh, Young Jin. Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 3, pp. 849-861. doi : 10.1007/s10587-012-0049-y. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0049-y/

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