Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator Is of Codazzi Type
Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 347-355

Voir la notice de l'article provenant de la source Cambridge University Press

We prove the non existence of real hypersurfaces in complex projective space whose structure Jacobi operator is of Codazzi type.
DOI : 10.4153/CMB-2007-033-9
Mots-clés : 53C15, 53B25
Pérez, Juan de Dios; Santos, Florentino G.; Suh, Young Jin. Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator Is of Codazzi Type. Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 347-355. doi: 10.4153/CMB-2007-033-9
@article{10_4153_CMB_2007_033_9,
     author = {P\'erez, Juan de Dios and Santos, Florentino G. and Suh, Young Jin},
     title = {Real {Hypersurfaces} in {Complex} {Projective} {Space} {Whose} {Structure} {Jacobi} {Operator} {Is} of {Codazzi} {Type}},
     journal = {Canadian mathematical bulletin},
     pages = {347--355},
     year = {2007},
     volume = {50},
     number = {3},
     doi = {10.4153/CMB-2007-033-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-033-9/}
}
TY  - JOUR
AU  - Pérez, Juan de Dios
AU  - Santos, Florentino G.
AU  - Suh, Young Jin
TI  - Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator Is of Codazzi Type
JO  - Canadian mathematical bulletin
PY  - 2007
SP  - 347
EP  - 355
VL  - 50
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-033-9/
DO  - 10.4153/CMB-2007-033-9
ID  - 10_4153_CMB_2007_033_9
ER  - 
%0 Journal Article
%A Pérez, Juan de Dios
%A Santos, Florentino G.
%A Suh, Young Jin
%T Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator Is of Codazzi Type
%J Canadian mathematical bulletin
%D 2007
%P 347-355
%V 50
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-033-9/
%R 10.4153/CMB-2007-033-9
%F 10_4153_CMB_2007_033_9

[1] [1] Chi, Q-S., A curvature characterization of certain locally rank-one symmetric spaces. J. Differential Geom. 28(1988), 187–202. Google Scholar

[2] [2] Cho, J-T. and Ki, U-H., Jacobi operators on real hypersurfaces of a complex projective space. Tsukuba J. Math. 22(1998), no. 1, 145–156. Google Scholar

[3] [3] Cho, J-T. and Ki, U-H., Real hypersurfaces of a complex projective space in terms of the Jacobi operators. Acta Math. Hungar. 80(1998), no. 1–2, 155–167. Google Scholar

[4] [4] Ki, U-H., Kim, H-J. and Lee, A-A., The Jacobi operator of real hypersurfaces in a complex space form. Commun. Korean Math. Soc. 13(1998), no. 3, 545–600. Google Scholar

[5] [5] Kim, H-J., A note on real hypersurfaces of a complex hyperbolic space. Tsukuba J. Math. 12(1988), no. 2, 451–457. Google Scholar

[6] [6] Kimura, M., Sectional curvatures of holomorphic planes on a real hypersurface in Pn (ℂ) . Math. Ann. 276(1987), no. 3, 487–497. Google Scholar

[7] [7] Kwon, J-H. and Nakagawa, H., A note on real hypersurfaces of complex projective space. J. Austral. Math. Soc. Ser. A 47(1989), no. 1, 108–113. Google Scholar

[8] [8] Loknherr, M. and Reckziegel, H., On ruled real hypersurfaces in complex space forms. Geom. Dedicata 74(1999), no. 3, 267–286. Google Scholar

[9] [9] Okumura, M., On some real hypersurfaces of a complex projective space. Trans. Amer.Math. Soc. 212(1975), 355–364. Google Scholar

[10] [10] Ortega, M., Perez, J. D. and Santos, F. G., Non-existence of real hypersurfaces with parallel structure Jacobi operator in nonflat complex space forms. Rocky Mountain J. Math. 36(2006), no. 5, 1603–1613. Google Scholar

[11] [11] Pérez, J. D. and Santos, F. G., On the Lie derivative of structure Jacobi operator of real hypersurfaces in complex projective space. Publ. Math. Debrecen, 66(2005), no. 3–4, 269–282. Google Scholar

[12] [12] Pérez, J. D. and Santos, F. G., Real hypersurfaces in complex projective space with recurrent structure Jacobi operator. To appear, Differential Geom. Appl. Google Scholar

[13] [13] Pérez, J. D., Santos, F. G. and Suh, Y. J., Real hypersurfaces in complex projective space whose structure Jacobi operator is Lie ξ-parallel. Differential Geom. Appl. 22(2005), no. 2, 181–188. Google Scholar

[14] [14] Pérez, J. D., Santos, F. G. and Suh, Y. J., Real hypersurfaces in complex projective space whose structure Jacobi operator is -parallel. Bull. Belgian Math. Soc. Simon Stevin 13(2006), no. 3, 459–469. Google Scholar

[15] [15] Takagi, R., On homogeneous real hypersurfaces in a complex projective space. Osaka J. Math. 10(1973), 495–506. Google Scholar

[16] [16] Takagi, R., Real hypersurfaces in a complex projective space with constant principal curvatures. J. Math. Soc. Japan 27(1975), 43–53. Google Scholar

[17] [17] Takagi, R., Real hypersurfaces in a complex projective space with constant principal curvatures. II. J. Math. Soc. Japan 27(1975), no. 4, 507–516. Google Scholar

Cité par Sources :