• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2089-2101
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• 2013

The aim of this paper is to introduce the notion of Lie recurrent structure Jacobi operator for real hypersurfaces in non-flat complex space forms and to study such real hypersurfaces. More precisely, the non-existence of such real hypersurfaces is proved.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.327-338
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• 2021

In this paper, we have introduced a new notion of recurrent structure Jacobi of real hypersurfaces in complex hyperbolic two-plane Grassmannians G^*₂(ℂ^m+2). Next, we show a non-existence property of real hypersurfaces in G^*₂(ℂ^m+2) satisfying such a curvature condition.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.849-861
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• 2023

In this paper, we introduce the notion of semi-symmetric structure Jacobi operator for Hopf real hypersufaces in the complex quadric Q^m = SO_m+2/SO_mSO₂. Next we prove that there does not exist any Hopf real hypersurface in the complex quadric Q^m = SO_m+2/SO_mSO₂ with semi-symmetric structure Jacobi operator. As a corollary, we also get a non-existence property of Hopf real hypersurfaces in the complex quadric Q^m with either symmetric (parallel), or recurrent structure Jacobi operator.