Geodesic
A Frankel type theorem for CR submanifolds of Sasakian manifolds
Archivum mathematicum, Tome 59 (2023) no. 5, pp. 369-381 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We prove a Frankel type theorem for $CR$ submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about $CR$ submanifolds of Sasakian space forms.
We prove a Frankel type theorem for $CR$ submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about $CR$ submanifolds of Sasakian space forms.
DOI : 10.5817/AM2023-5-369
Classification : 53C25, 53C40
Keywords: intersection of submanifolds; CR submanifold of a Sasakian manifold; scalar Levi form 
@article{10_5817_AM2023_5_369,
     author = {Di Pinto, Dario and Lotta, Antonio},
     title = {A {Frankel} type theorem for {CR} submanifolds of {Sasakian} manifolds},
     journal = {Archivum mathematicum},
     pages = {369--381},
     year = {2023},
     volume = {59},
     number = {5},
     doi = {10.5817/AM2023-5-369},
     mrnumber = {4641952},
     zbl = {07790553},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2023-5-369/}
}
TY  - JOUR
AU  - Di Pinto, Dario
AU  - Lotta, Antonio
TI  - A Frankel type theorem for CR submanifolds of Sasakian manifolds
JO  - Archivum mathematicum
PY  - 2023
SP  - 369
EP  - 381
VL  - 59
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2023-5-369/
DO  - 10.5817/AM2023-5-369
LA  - en
ID  - 10_5817_AM2023_5_369
ER  - 
%0 Journal Article
%A Di Pinto, Dario
%A Lotta, Antonio
%T A Frankel type theorem for CR submanifolds of Sasakian manifolds
%J Archivum mathematicum
%D 2023
%P 369-381
%V 59
%N 5
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2023-5-369/
%R 10.5817/AM2023-5-369
%G en
%F 10_5817_AM2023_5_369
Di Pinto, Dario; Lotta, Antonio. A Frankel type theorem for CR submanifolds of Sasakian manifolds. Archivum mathematicum, Tome 59 (2023) no. 5, pp. 369-381. doi: 10.5817/AM2023-5-369

[1] Bejancu, A.: Geometry of CR-submanifolds. Mathematics and its Applications (East European Series), vol. 23, D. Reidel Publishing Co., Dordrecht, 1986. | MR | Zbl

[2] Bejancu, A., Papaghiuc, N.: Semi-invariant submanifolds of a Sasakian manifold. An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 27 (1981), 163–170. | MR

[3] Binh, T.Q., Ornea, L., Tamássy, L.: Intersections of Riemannian submanifolds. Variations on a theme by T.J. Frankel. Rend. Mat. Appl. (7) 19 (1999), 107–121. | MR

[4] Blair, D.E.: Riemannian Geometry of Contact and Symplectic Manifolds. second ed., Progress in Mathematics, vol. 203, Birkhäuser, Boston, 2010. | MR | Zbl

[5] Djorić, M., Okumura, M.: CR submanifolds of complex projective space. Developments in Mathematics, vol. 19, Springer, New York, 2010. | DOI | MR

[6] Falcitelli, M., Ianus, S., Pastore, A.M.: Riemannian submersions and related topics. World Scientific Publishing Co., Singapore, 2004. | MR

[7] Frankel, T.: Manifolds with positive curvature. Pacific J. Math. 11 (1961), 165–171. | DOI | MR

[8] Goldberg, S.I., Kobayashi, S.: Holomorphic bisectional curvature. J. Differential Geom. 1 (1967), 225–233. | DOI | MR

[9] Medori, C., Nacinovich, M.: Levi-Tanaka algebras and homogeneous CR manifolds. Compositio Math. 109 (1997), 195–250. | DOI | MR

[10] Pitis, G.: On the topology of Saskian manifolds. Math. Scand. 93 (2003), 99–108. | DOI | MR

[11] Sakai, T.: Riemannian Geometry. Translations of Mathematical Monographs, vol. 149, Amer. Math. Soc., Providence, 1996. | MR

[12] Takahashi, T.: Sasakian $\phi $-symmetric spaces. Tôhoku Math. J. 29 (1977), 91–113. | DOI | MR

[13] Tanno, S., Baik, S.-B.: $\phi $-holomorphic special bisectional curvature. Tôhoku Math. J. 22 (1970), 184–190. | DOI | MR

[14] Yano, K., Kon, M.: Generic submanifolds of Sasakian manifolds. Kodai Math. J. 3 (1980), 163–196. | DOI | MR

[15] Yano, K., Kon, M.: CR submanifolds of Kaehlerian and Sasakian manifolds. Progress in Mathematics, vol. 30, Birkhäuser, Boston, Mass., 1983. | MR

[16] Yano, K., Kon, M.: Structures on Manifolds. Series in Pure Mathematics, vol. 3, World Scientific Publishing Co., Singapore, 1984. | MR | Zbl

Cité par Sources :