On Characterizations of Real Hypersurfaces in a Complex Space Form with η-Parallel Shape Operator
Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 114-126

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

In this paper we study real hypersurfaces in a non-flat complex space form with $\eta $ -parallel shape operator. Several partial characterizations of these real hypersurfaces are obtained.
DOI : 10.4153/CMB-2011-039-5
Mots-clés : 53C40, 53C15, complex space form, Hopf hypersurfaces, ruled real hypersurfaces, η-parallel shape operator
Kon, S. H.; Loo, Tee-How. On Characterizations of Real Hypersurfaces in a Complex Space Form with η-Parallel Shape Operator. Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 114-126. doi: 10.4153/CMB-2011-039-5
@article{10_4153_CMB_2011_039_5,
     author = {Kon, S. H. and Loo, Tee-How},
     title = {On {Characterizations} of {Real} {Hypersurfaces} in a {Complex} {Space} {Form} with {\ensuremath{\eta}-Parallel} {Shape} {Operator}},
     journal = {Canadian mathematical bulletin},
     pages = {114--126},
     year = {2012},
     volume = {55},
     number = {1},
     doi = {10.4153/CMB-2011-039-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-039-5/}
}
TY  - JOUR
AU  - Kon, S. H.
AU  - Loo, Tee-How
TI  - On Characterizations of Real Hypersurfaces in a Complex Space Form with η-Parallel Shape Operator
JO  - Canadian mathematical bulletin
PY  - 2012
SP  - 114
EP  - 126
VL  - 55
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-039-5/
DO  - 10.4153/CMB-2011-039-5
ID  - 10_4153_CMB_2011_039_5
ER  - 
%0 Journal Article
%A Kon, S. H.
%A Loo, Tee-How
%T On Characterizations of Real Hypersurfaces in a Complex Space Form with η-Parallel Shape Operator
%J Canadian mathematical bulletin
%D 2012
%P 114-126
%V 55
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-039-5/
%R 10.4153/CMB-2011-039-5
%F 10_4153_CMB_2011_039_5

[1] [1] Ahn, S.-S., Lee, S. B., and Suh, Y. J., On ruled real hypersurfaces in a complex space form. Tsukuba J. Math. 17(1993), no. 2, 311–322. Google Scholar

[2] [2] Berndt, J., Real hypersurfaces with constant principal curvatures in complex hyperbolic space. J. Reine Angew Math. 395(1989), 132–141. Google Scholar

[3] [3] Choe, Y.-W., Characterization of certain real hypersurfaces of a complex space form. Nihonkai Math. J. 6(1995), no. 1, 97–114. Google Scholar

[4] [4] Ki, U.-H. and Suh, Y. J., On a characterization of real hypersurfaces of type A in a complex space form. Canad. Math. Bull. 37(1994), no. 2, 238–244. doi:10.4153/CMB-1994-035-8 Google Scholar

[5] [5] Kim, I.-B., Kim, K. H. and Sohn, W. H., Characterizations of real hypersurfaces in a complex space form. Canad. Math. Bull. 50(2007), no. 1, 97–104. doi:10.4153/CMB-2007-009-5 Google Scholar

[6] [6] Kim, H. S. and Pyo, Y.-S., On real hypersurfaces of type A in a complex space form. III. Balkan J. Geom. Appl. 3(1998), no. 2, 101–110. Google Scholar

[7] [7] Kimura, M., Real hypersurfaces and complex submanifolds in complex projective space. Trans. Amer. Math. Soc. 296(1986), no. 1, 137–149. doi:10.1090/S0002-9947-1986-0837803-2 Google Scholar

[8] [8] Kimura, M. and Maeda, S., On real hypersurfaces of a complex projective space. Math. Z. 202(1989), no. 3, 299–311. doi:10.1007/BF01159962 Google Scholar

[9] [9] Kon, M., Pseudo-Einstein real hypersurfaces in complex space forms. J. Diff. Geom. 14(1979), no. 3, 339–354. Google Scholar

[10] [10] Lohnherr, M. and Reckziegel, H., On ruled real hypersurfaces in complex space forms. Geom. Dedicata. 74(1999), no. 3, 267–286. doi:10.1023/A:1005000122427 Google Scholar

[11] [11] Maeda, Y., On real hypersurfaces of a complex projective space. J. Math. Soc. Japan 28(1976), no. 3, 529–540. doi:10.2969/jmsj/02830529 Google Scholar

[12] [12] Montiel, S. and Romero, A., On some real hypersurfaces of a complex hyperbolic space. Geom. Dedicata. 20(1986), no. 2, 245–261. Google Scholar

[13] [13] Niebergall, R. and Ryan, P. J., Real hypersurfaces in complex space forms. In : Tight and Taut Submanifolds, Math. Sci., Res. Inst. Publ. 32, Cambrigde University Press, Cambridge, 1997, pp. 233–305. Google Scholar

[14] [14] Okumura, M., Contact hypersurfaces in certain Kaehlerian manifolds. Tohoku Math. J. 18(1966), 74–102. doi:10.2748/tmj/1178243483 Google Scholar

[15] [15] Okumura, M., On some real hypersurfaces of a complex projective space. Trans. Amer. Math. Soc. 212(1975), 355–364. doi:10.1090/S0002-9947-1975-0377787-X Google Scholar

[16] [16] Suh, Y. J., Characterizations of real hypersurfaces in complex space forms in terms of Weingarten map. Nihonkai Math. J. 6(1995), no. 1, 63–79. Google Scholar

[17] [17] Suh, Y. J., On real hypersurfaces of a complex space form with η-parallel Ricci tensor. Tsukuba J. Math. 14(1990), no. 1, 27–37. Google Scholar

[18] [18] Takagi, R., On homogeneous real hypersurfaces in a complex projective space. Osaka J. Math. 10(1973), 495–506. Google Scholar

[19] [19] Vernon, M. H., Contact hypersurfaces of a complex hyperbolic space. Tohoku Math. J. 39(1987), no. 2, 215–222. doi:10.2748/tmj/1178228324 Google Scholar

Cité par Sources :