Ideal CR submanifolds in non-flat complex space forms
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 79-90
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

An explicit representation for ideal CR submanifolds of a complex hyperbolic space has been derived in T. Sasahara (2002). We simplify and reformulate the representation in terms of certain Kähler submanifolds. In addition, we investigate the almost contact metric structure of ideal CR submanifolds in a complex hyperbolic space. Moreover, we obtain a codimension reduction theorem for ideal CR submanifolds in a complex projective space.
An explicit representation for ideal CR submanifolds of a complex hyperbolic space has been derived in T. Sasahara (2002). We simplify and reformulate the representation in terms of certain Kähler submanifolds. In addition, we investigate the almost contact metric structure of ideal CR submanifolds in a complex hyperbolic space. Moreover, we obtain a codimension reduction theorem for ideal CR submanifolds in a complex projective space.
DOI : 10.1007/s10587-014-0085-x
Classification : 32V40, 53B25, 53C40, 53C42
Keywords: $\delta $-invariants; CR submanifolds; ideal submanifolds
@article{10_1007_s10587_014_0085_x,
     author = {Sasahara, Toru},
     title = {Ideal {CR} submanifolds in non-flat complex space forms},
     journal = {Czechoslovak Mathematical Journal},
     pages = {79--90},
     year = {2014},
     volume = {64},
     number = {1},
     doi = {10.1007/s10587-014-0085-x},
     mrnumber = {3247446},
     zbl = {06391478},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0085-x/}
}
TY  - JOUR
AU  - Sasahara, Toru
TI  - Ideal CR submanifolds in non-flat complex space forms
JO  - Czechoslovak Mathematical Journal
PY  - 2014
SP  - 79
EP  - 90
VL  - 64
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0085-x/
DO  - 10.1007/s10587-014-0085-x
LA  - en
ID  - 10_1007_s10587_014_0085_x
ER  - 
%0 Journal Article
%A Sasahara, Toru
%T Ideal CR submanifolds in non-flat complex space forms
%J Czechoslovak Mathematical Journal
%D 2014
%P 79-90
%V 64
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0085-x/
%R 10.1007/s10587-014-0085-x
%G en
%F 10_1007_s10587_014_0085_x
Sasahara, Toru. Ideal CR submanifolds in non-flat complex space forms. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 79-90. doi: 10.1007/s10587-014-0085-x

[1] Chen, B. Y.: CR-submanifolds of a Kähler manifold. I. J. Differ. Geom. 16 (1981), 305-322. | DOI | MR | Zbl

[2] Chen, B. Y.: CR-submanifolds of a Kähler manifold. II. J. Differ. Geom. 16 (1981), 493-509. | DOI | MR

[3] Chen, B. Y.: Some new obstructions to minimal and Lagrangian isometric immersions. Jap. J. Math., New Ser. 26 (2000), 105-127. | DOI | MR | Zbl

[4] Chen, B. Y.: Pseudo-Riemannian Geometry, $\delta$-Invariants and Applications. World Scientific, Hackensack, NJ (2011). | MR | Zbl

[5] Chen, B. Y., Ludden, G. D., Montiel, S.: Real submanifolds of a Kähler manifold. Algebras Groups Geom. 1 (1984), 176-212. | MR

[6] Djorić, M., Okumura, M.: CR Submanifolds of Complex Projective Space. Developments in Mathematics 19. Springer, Berlin (2010). | DOI | MR | Zbl

[7] Okumura, M.: Codimension reduction problem for real submanifolds of complex projective space. Differential Geometry and Its Applications (Eger, 1989) Colloq. Math. Soc. János Bolyai 56. North-Holland Amsterdam (1992), 573-585. | MR

[8] Sasahara, T.: On Ricci curvature of CR-submanifolds wit rank one totally real distribution. Nihonkai Math. J. 12 (2001), 47-58. | MR

[9] Sasahara, T.: On Chen invariant of CR-submanifolds in a complex hyperbolic space. Tsukuba J. Math. 26 (2002), 119-132. | DOI | MR | Zbl

Cité par Sources :