Abstract
In this paper, we prove that if \((\nabla _{X} L_{\xi })Y= (\nabla _{Y} L_{\xi })X\) holds on \(M\), then \(M\) is a Hopf hypersurface, where \(L_\xi \) denote the induced operator from the Lie derivative with respect to the structure vector field \(\xi \). We characterize such Hopf hypersurfaces of \(M_n(c)\).
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The authors would like to express their sincere gratitude to the referee who gave them valuable suggestions and comments.
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Communicated by D. V. Alekseevsky.
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Lim, D.H., Sohn, W.H. On characterizations of real hypersurface in complex space form with Codazzi type structure Lie operator. Monatsh Math 173, 371–378 (2014). https://doi.org/10.1007/s00605-013-0579-x
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DOI: https://doi.org/10.1007/s00605-013-0579-x