JP Journal of Geometry and Topology

The JP Journal of Geometry and Topology publishes articles in all branches of geometry and topology, with applications to physics. It covers areas such as differential geometry, algebraic topology, and geometric aspects of mathematical physics. Survey articles are also welcome.

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LIE $\xi$-DERIVATIVE OF STRUCTURE TENSOR FIELD ON REAL HYPERSURFACES IN A NON-FLAT COMPLEX SPACE FORM

Authors

  • Dong Ho Lim
  • Hoonjoo Kim

Keywords:

real hypersurface, structure tensor field, model space of type A, Lie derivative

DOI:

https://doi.org/10.17654/0972415X25002

Abstract

In this paper, we characterize a real hypersurface in a non-flat complex space form whose structure tensor field and the Lie derivative in the direction of the Reeb vector field either commute or anti-commute.

Received: October 18, 2024
Revised: January 19, 2025
Accepted: January 28, 2025

References

J. Berndt, Real hypersurfaces with constant principal curvatures in complex hyperbolic space, J. Reine Angew. Math. 395 (1989), 132-141.

U-H. Ki and Y. J. Suh, On real hypersurfaces of a complex space form, J. Okayama Univ. 32 (1990), 207-221.

U-H. Ki and Y. J. Suh, Characterizations of some real hypersurfaces in a complex space form in terms of Lie derivative, J. Korean Math. Soc. 32(2) (1995), 161 170.

S. Maeda and S. Udagawa, Real hypersurfaces of a complex projective space in terms of holomorphic distribution, Tsukuba J. Math. 14 (1990), 39-52.

S. Montiel and A. Romero, On some real hypersurfaces of a complex hyperbolic space, Geom. Dedicata 20 (1986), 245-261.

R. Niebergall and P. J. Ryan, Real Hypersurfaces in Complex Space Forms, Tight and Taut Submanifolds, Cambridge Univ. Press, 1998, pp. 233-305.

M. Okumura, On some real hypersurfaces of a complex projective space, Trans. Amer. Math. Soc. 212 (1975), 355-364.

R. Takagi, On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math. 10 (1973), 495-506.

W. Wang, A characterization of ruled hypersurfaces in complex space forms in terms of the Lie derivative of shape operator, AIMS Math. 6 (2021), 14054-14063.

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Published

2025-03-21

Issue

Vol. 31 No. 1 (2025)

Section

Articles

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How to Cite

LIE $\xi$-DERIVATIVE OF STRUCTURE TENSOR FIELD ON REAL HYPERSURFACES IN A NON-FLAT COMPLEX SPACE FORM. (2025). JP Journal of Geometry and Topology, 31(1), 11-18. https://doi.org/10.17654/0972415X25002

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