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Real hypersurfaces in a non-flat complex space form with Lie recurrent structure Jacobi operator

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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.

Abstract

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.

참고문헌 (12)

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  3. T. A. Ivey, "The structure Jacobi operator for real hypersurfaces in CP2 and CH2", Results Math, 56(1), pp.473~488 (2009)
  4. R. Niebergall, "Real hypersurfaces in complex space forms, Tight and taut submanifolds, In Math. Sci. Res. Inst. Publ., 32", pp.233~305 (1997), Cambridge Univ. Press
  5. K. Panagiotidou Ph, "Real hypersurfaces in CP2 and CH2 whose structure Jacobi operator is Lie D-parallel", Note Mat, 32(2), pp.89~99 (2012)
  6. J. D. Perez, "On the Lie derivative of structure Jacobi operator of real hypersurfaces in complex projective space", Publ. Math. Debrecen, 66(3), pp.269~282 (2005)
  7. J. D. Perez, "Real hypersurfaces in complex projective space with recurrent structure Jacobi operator", Diff. Geom. And its Appl, 26(2), pp.218~223 (2008)
  8. J. D. Perez, "Real hypersurfaces in complex projective space whose structure Jacobi operator is Lie ξ-parallel", Diff. Geom. And its Appl, 22(2), pp.181~188 (2005)
  9. J. D. Perez, "Real hypersurfaces in a complex projective space whose structure Jacobi operator is Lie D-parallel", Canad. Math. Bull, 56, pp.306~316 (2013)
  10. R. Takagi, "On homogeneous real hypersurfaces in a complex projective space", Osaka J. Math, 10, pp.495~506 (1973)
  11. R. Takagi, "Real hypersurfaces in a complex projective space with constant principal curvatures", J. Math. Soc. Japan, 27, pp.43~53 (1975)
  12. Th. Theofanidis, "Non-existence of real hypersurfaces equipped with recurrent structure Jacobi operator in nonflat complex space forms", Results Math, 61(1), pp.43~55 (2012)

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