Geodesic
Totally real surfaces of the six-dimensional sphere
Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 83-87

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

An almost Hermitian manifold (, J, g) with Riemannian connection is called nearly Kaehlerian if (xJ)X = 0 for any . The typical example is the sphere S6. The nearly Kaehlerian structure J for S6 is constructed in a natural way by making use of Cayley division algebra [3]. It is because of this nearly Kaehler, non-Kaehler, structure that S6 has attracted attention. Different classes of submanifolds of S6 have been considered by A. Gray [4], K. Sekigawa [5] and N. Ejiri [2]. In this paper we study 2-dimensional totally real submanifolds of S6. These are submanifolds with the property that for every x є M, J (Tx M) belongs to the normal bundle v. For this class we have obtained the following result. 
Bashir, M. A. Totally real surfaces of the six-dimensional sphere. Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 83-87. doi: 10.1017/S0017089500008065
@article{10_1017_S0017089500008065,
     author = {Bashir, M. A.},
     title = {Totally real surfaces of the six-dimensional sphere},
     journal = {Glasgow mathematical journal},
     pages = {83--87},
     year = {1991},
     volume = {33},
     number = {1},
     doi = {10.1017/S0017089500008065},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008065/}
}
TY  - JOUR
AU  - Bashir, M. A.
TI  - Totally real surfaces of the six-dimensional sphere
JO  - Glasgow mathematical journal
PY  - 1991
SP  - 83
EP  - 87
VL  - 33
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008065/
DO  - 10.1017/S0017089500008065
ID  - 10_1017_S0017089500008065
ER  - 
%0 Journal Article
%A Bashir, M. A.
%T Totally real surfaces of the six-dimensional sphere
%J Glasgow mathematical journal
%D 1991
%P 83-87
%V 33
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008065/
%R 10.1017/S0017089500008065
%F 10_1017_S0017089500008065

[1] 1.Dillen, F., Verstraelen, L. and Vrancken, L., Classification of totally real 3-dimensional submanifolds of s 6(1) with K ≥ , preprint. Google Scholar

[2] 2.Ejiri, N., Totally real submanifolds in a 6-sphere, Proc. Amer. Math. Soc. 83 (1981), 759–763. Google Scholar | DOI

[3] 3.Fukami, T. and Ishihara, S., Almost Hermitian structure on S 6, Tohoku Math. J. 7 (1955), 151–156. Google Scholar | DOI

[4] 4.Gray, A., Almost complex submanifolds of the six sphere, Proc. Amer. Math. Soc. 20 (1969), 277–279. Google Scholar | DOI

[5] 5.Sekigawa, K., Almost complex submanifolds of a 6-dimensional sphere, Kodai Math. J. 6 (1983), 174–185. Google Scholar | DOI

[6] 6.Spivak, M., A comprehensive introduction to differential geometry (Publish or Perish Inc., 1979). Google Scholar

Cité par Sources :