Open Access
Research Article
Submersions of Contact CR-Submanifolds of Generalized Quasi Sasakian Manifolds
*Mohd Danish SiddiqiCorresponding authormsiddiqi@jazanu.edu.saDepartment of MathematicsFaculty of ScienceJazan UniversityJizan, Kingdom of Saudi ArabiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 May 2018
- Accepted:
- 11 Feb 2019
- Published Online:
- 29 Jul 2020
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- 1726037X.2020.1796247
- Pages:
- 81–95
Abstract
In this paper, we discuss some properties of almost contact metric submersion of contact CR-submanifolds of generalized quasi-Sasakian manifold and derive some results based on their curvatures’s differential geometry. We also study de-Rham cohomology of CR-submanifold of generalized quasi-Sasakian manifold under the submersion.
Keywords
Subject Classifications
53C2553C2053C5053C40
References
- A.Bejancu, Geometry of -submanifold, D. Reidel publishing company, Holland, 1986 .
- D. E.Blair, Contact manifold in Riemannian geometry , Lectur Notes in Math, 59, Sprinnger Verlag , 1976 .
- B.Chen, Cohomology of -submanifolds , Ann. Fac. Sci. Toulouse Math. 3 (5), no. 2 , 167 - 172 , 1981 . doi: 10.5802/afst.566
- C.Chinea, Almost contact metric submersions , Rend. Circ. Mat. Palermo , 43 ( 1 ), 89 - 104 , 1985 . doi: 10.1007/BF02844887
- M.Falcitelli, S.Ianus, A. M.Pastore and M.Visinescu, Some applications of Riemannian submersion in physics , Rev. Roum. Phys . 48 , 627 - 639 , 2003 .
- S.Kobayashi, Submersion of -submanifolds , Tohoku Math. J. 39 ( 2 ), no. 1 , 95 - 100 , 1987 .
- K.Kenmotsu, A class of almost contact Riemannian manifolds Tohoku Math. J. 24 ( 2 ), 93 - 103 , 1972 .
- F.Massamba, T. T.Matamba., Horizontally submersions of contact R-submanifolds . Turkish Journal of Mathematics , 38 , 436 453 , 2014 .
- B.O’Neill. The fundamental equations of a submersions , Mich. Math. J. , 13 , 458 - 469 , 1996 .
- B.O’Neill, Semi-Riemannian Geometry with Applications to Relativity , Academic Press , 1983 .
- N.Papaghiuc, Submersion of semi-invariant submanifolds of a Sasakian manifold , An. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat . 35 , no. 3 21 - 288 , 1989 .
- M.Visinescu, Space-time compactification induced by nonlinear sigma models, gauge fields and submersions , Czechoslovak J . Phys. B 37 , no. 4 , 525 - 528 , 1987 .
- M. D.Siddiqi, A.Haseeb and M.Ahmad, Skew Semi-invariant Submanifolds of Generalized Quasi-Sasakian Manifolds , Carpathian Math. Publ ., 9 ( 2 ), 188 - 197 , 2017 . doi: 10.15330/cmp.9.2.188-197
- M. H.Shahid, F. R.Al-Solamy, J. B.Jun and M.Ahamd, Submersion of Semi-Invariant Submanifolds of Trans-Sasakian Manifold , Bull. Malays. Math. Sci. Soc . ( 2 ) 36 (1) 6371 , 2013 .
- M. H.Shahid, F. R.Al-Solamy and M.Jamali, Submersions of Submanifolds. In: Dragomir S., Shahid M., Al-Solamy F. (eds) Geometry of Cauchy-Riemann Submanifolds. Springer, Singapore (2016) .
- B.Watson, B., Riemannian submersions and nonlinear gauge field equation of general relativity, in Global Analysis-Analysis on Manifolds, 324-349, Teubner-Texte Math., 57 Teubner, Leizig, 1983 .
- K.Yano and M.Kon, M. Contact -submanifolds , Kodai Math. J. , 5 ( 2 ), 238 - 252 , 1982 . doi: 10.2996/kmj/1138036553
- R.Shamsur and Ahmad. A., On the geometry of hypersurfaces of a certain connection in a Quasi-Sasakian manifold . International J.Math. Combin ., 3 ( 2011 ), 23 - 33 .
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