| Title:
|
Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms (English) |
| Author:
|
Hui, Shyamal K. |
| Author:
|
Lemence, Richard S. |
| Author:
|
Mandal, Pradip |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
105-117 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A submanifold $M^m$ of a generalized Sasakian-space-form $\overline{M}^{2n+1}(f_1,\allowbreak f_2,f_3)$ is said to be $C$-totally real submanifold if $\xi\in \Gamma(T^\bot M)$ and $\phi X\in \Gamma(T^\bot M)$ for all $X\in \Gamma(TM)$. In particular, if $m=n$, then $M^n$ is called Legendrian submanifold. Here, we derive Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms with respect to different connections; namely, quarter symmetric metric connection, Schouten-van Kampen connection and Tanaka-Webster connection. (English) |
| Keyword:
|
generalized Sasakian-space-form |
| Keyword:
|
Legendrian submanifold |
| MSC:
|
53C15 |
| MSC:
|
53C25 |
| idZBL:
|
Zbl 07217162 |
| idMR:
|
MR4093433 |
| DOI:
|
10.14712/1213-7243.2020.006 |
| . |
| Date available:
|
2020-04-30T11:22:24Z |
| Last updated:
|
2022-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148079 |
| . |
| Reference:
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[1] Alegre P., Blair D. E., Carriazo A.: Generalized Sasakian-space-forms.Israel J. Math. 141 (2004), 157–183. MR 2063031, 10.1007/BF02772217 |
| Reference:
|
[2] Alegre P., Carriazo A.: Structures on generalized Sasakian-space-forms.Differential Geom. Appl. 26 (2008), no. 6, 656–666. MR 2474428, 10.1016/j.difgeo.2008.04.014 |
| Reference:
|
[3] Bejancu A.: Schouten–van Kampen and Vrănceanu connections on foliated manifolds.An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 52 (2006), no. 1, 37–60. MR 2282431 |
| Reference:
|
[4] Blair D. E.: Contact Manifolds in Riemannian Geometry.Lecture Notes in Mathematics, 509, Springer, Berlin, 1976. MR 0467588 |
| Reference:
|
[5] Carriazo A.: On generalized Sasakian-space-forms.Proc. of the Ninth International Workshop on Differential Geometry, Kyungpook Nat. Univ., Taegu, (2005), 31–39. MR 2136149 |
| Reference:
|
[6] Gołab S.: On semi-symmetric and quarter-symmetric linear connections.Tensor (N.S.) 29 (1975), no. 3, 249–254. MR 0383275 |
| Reference:
|
[7] Lu Z.: Normal scalar curvature conjecture and its applications.J. Funct. Anal. 261 (2011), no. 5, 1248–1308. MR 2807100 |
| Reference:
|
[8] Mihai I.: On the generalized Wintgen inequality for Lagrangian submanifolds in complex space forms.Nonlinear Anal. 95 (2014), 714–720. MR 3130556, 10.1016/j.na.2013.10.009 |
| Reference:
|
[9] Mihai I.: On the generalized Wintgen inequality for Legendrian submanifolds in Sasakian space forms.Tohoku Math. J. (2) 69 (2017), no. 1, 43–53. MR 3640013, 10.2748/tmj/1493172127 |
| Reference:
|
[10] Olszak Z.: The Schouten van-Kampen affine connection adapted to an almost (para) contact metric structure.Publ. Inst. Math. (Beograd) (N.S.) 94(108) (2013), 31–42. MR 3137487, 10.2298/PIM1308031O |
| Reference:
|
[11] Schouten J. A., van Kampen E. R.: Zur Einbettungs- und Krümmungstheorie nichtholonomer Gebilde.Math. Ann. 103 (1930), 752–783 (German). MR 1512645, 10.1007/BF01455718 |
| Reference:
|
[12] Tanaka, N.: On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections.Japan J. Math. (N.S.) 2 (1976), no. 1, 131–190. MR 0589931, 10.4099/math1924.2.131 |
| Reference:
|
[13] Tanno, S.: Variational problems on contact Riemannian manifolds.Trans. Amer. Math. Soc. 314 (1989), no. 1, 349–379. MR 1000553, 10.1090/S0002-9947-1989-1000553-9 |
| Reference:
|
[14] Webster S. M.: Pseudo-Hermitian structures on a real hypersurface.J. Differential Geometry 13 (1978), no. 1, 25–41. MR 0520599, 10.4310/jdg/1214434345 |
| Reference:
|
[15] Wintgen P.: Sur l'inégalité de Chen-Willmore.C. R. Acad. Sci. Paris Sér. A-B 288 (1979), no. 21, A993–A995 (French. English summary). MR 0540375 |
| Reference:
|
[16] Yano K., Kon M.: Anti-invariant Submanifolds.Lecture Notes in Pure and Applied Mathematics, 21, Marcel Dekker, New York, 1976. MR 0425849 |
| Reference:
|
[17] Yano K., Kon M.: Structures on Manifolds.Series in Pure Mathematics, 3, World Scientific Publishing, Singapore, 1984. MR 0794310 |
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