Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator Is Cyclic-Ryan Parallel

• Journal title : Kyungpook mathematical journal
• Volume 49, Issue 2,  2009, pp.211-219
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2009.49.2.211
Title & Authors
Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator Is Cyclic-Ryan Parallel
De Dios Perez, Juan; Santos, Florentino Garcia;

Abstract
We classify real hypersurfaces in complex projective space whose structure Jacobi operator satisfies a certain cyclic condition.
Keywords
complex projective space;real hypersurface;structure Jacobi operator;cyclic Ryan parallelness;
Language
English
Cited by
1.
Semi-parallelism of normal Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians, Monatshefte für Mathematik, 2013, 172, 2, 167
2.
Semi-parallel symmetric operators for Hopf hypersurfaces in complex two-plane Grassmannians, Monatshefte für Mathematik, 2015, 177, 4, 539
References
1.
Q. S. Chi, A curvature characterization of certain locally rank-one symmetric spaces, J. Diff. Geom., 28(1988), 187-202.

2.
J. T. Cho and U-H. Ki, Jacobi operators on real hypersurfaces of a complex projective space, Tsukuba J. Math., 22(1998), 145-156.

3.
J. T. Cho and U-H. Ki, Real hypersurfaces of a complex projective space in terms of the Jacobi operators, Acta Math. Hungar., 80(1998), 155-167.

4.
U-H. Ki, H.J. Kim and A.A. Lee, The Jacobi operator of real hypersurfaces in a complex Space form, Commun. Korean Math. Soc., 13(1998), 545-600.

5.
M. Kimura, Sectional curvatures of holomorphic planes on a real hypersurface in $P^n(C)$, Math. Ann., 276(1987), 487-497.

6.
M. Kimura and S. Maeda, On real hypersurfaces of a complex projective space III, Hokkaido Math. J., 22(1993), 63-78.

7.
M. Loknherr and H. Reckziegel, On ruled real hypersurfaces in complex space forms, Geom. Dedicata, 74(1999), 267-286.

8.
M. Okumura, On some real hypersurfaces of a c omplex projective space, Trans. A. M. S., 212(1975), 355-364.

9.
M. Ortega, J. D. Perez and F. G. Santos, Non-existence of real hypersurfaces with parallel structure Jacobi operator in nonflat complex space forms, Rocky Mountain J. Math., 36(2006), 1603-1613.

10.
J. D. Perez and F. G. Santos, On the Lie derivative of structure Jacobi operator of real hypersurfaces in complex projective space, Publ. Math. Debrecen, 66(2005), 269-282.

11.
J. D. Perez and F. G. Santos, Real hypersurfaces in complex projective space with recurrent structure Jacobi operator, Diff. Geom. Appl., 26(2008), 218-223.

12.
J. D. Perez, F. G. Santos and Y. J. Suh, Real hypersurfaces in complex projective space whose structure Jacobi operator is Lie $\varepsilon$-parallel, Diff. Geom. Appl., 22(2005),181-188.

13.
J. D. Perez, F. G. Santos and Y. J. Suh, Real hypersurfaces in complex projective space whose structure Jacobi operator is D-parallel, Bull. Belgian Math. Soc. Simon Stevin, 13(2006), 459-469.

14.
R. Takagi, On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math., 10(1973), 495-506.

15.
R. Takagi, Real hypersurfaces in complex projective space with constant principal curvatures, J. Math. Soc. Japan, 27(1975), 43-53.

16.
R. Takagi, Real hypersurfaces in complex projective space with constant principal curvatures II, J. Math. Soc. Japan, 27(1975), 507-516.