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On geometry of warped product semi invariant submanifolds of nearly (ε, δ)-trans sasakian manifold with a certain connection | ||
| Journal of Hyperstructures | ||
| دوره 12، شماره 1، شهریور 2023، صفحه 158-172 اصل مقاله (301.17 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2023.2519 | ||
| نویسندگان | ||
| Shamsur Rahman1؛ Sabi Ahmad* 2؛ Niranjan Kumar Mishra2 | ||
| 1Faculty of Mathematics, Maulana Azad National Urdu University, Polytechnic of Campus Darbhanga Bihar- 846002, India | ||
| 2Department of Mathematics, University of RKDF, Ranchi, Jharkhand 834004, Ranchi, India | ||
| چکیده | ||
| In this paper, we study the geometry of warped product semi invariant submanifold of a nearly (ε, δ)-trans-Sasakian manifold M with a quarter symmetric non metric connection. We see that warped product of the typeE⊥×yET is a usual Riemannian product of E⊥ and ET , where E⊥ and ET are anti-invariant and invariant submanifolds of a nearly (ε, δ)-trans-Sasakian manifold with a quarter symmetric non metric connection M, respectively. We also obtain a characterization for such type of warped product. | ||
| کلیدواژه‌ها | ||
| Warped product؛ semi-invariant submanifolds؛ nearly $(\varepsilon؛ \delta )$-trans-Sasakian manifold | ||
| مراجع | ||
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[1] R.L. Bishop and B. O Neill, Manifolds of Negative curvature, Trans. Amer. Math.Soc., 145 (1969), 149 . [2] B. Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifold,Monatsh. Math., 133 (2001), 177195. [3] B.Y. Chen Geometry of warped product CR-submanifolds in Kaehler manifolds.II , Monatshefte f¨ur Mathematik, 134 (2) (2001), 103119. [4] At¸ceken, M., Warped product semi-invariant submanifolds in almost paracontact Riemannian manifolds, Mathematical Problems in Engineering, 2009 (2009) Article ID 621625, 16 pages. [5] D. E. Blair, Almost contact manifolds with Killing structure tensors, Pacific Jour-nal of Mathematics, 39 (1971), 285292. [6] S. Hiepko, , Eine innere Kennzeichnung der verzerrten produkte, Mathematische Annalen, 241 (3) (1979), 209215. [7] S. Rahman, A.K. Rai, A. Horaira and M. S. Khan On warped product semi invariant submanifolds of nearly (ε, δ)-trans Sasakian manifold, Bulletin of the Transilvania University of Brasov Series III: Mathematics, Informatics, Physics, 13 (62), 1, (2020), 247-260. [8] A. Bejancu, Geometry of CR-submanifolds, D. Reidel Publ. Co., Holland, 1986. [9] K. Yano and M. Kon, CR submanifolds of Kaehlerian and Sasakian manifolds, Birkhauser, Boston, 1983. [10] Rahman, S., and Ahmad, A., On semi-invariant submanifolds of a nearly transhyperbolic Sasakan manifold, Malaya Journal of Matematik 3 (3) (2015), 303311. [11] Rahman, S.,Jun, B. J., and Ahmad A., On semi-invariant submanifolds of a nearly Lorentzian para-Sasakian manifold, Far East Journal of Mathematical Sciences, 96 (6) (2015), 709-724. [12] Rahman, S. Rai, A.K. , Horaira, A. and Khan M. S. On warped product semi invariant submanifolds of nearly (ε, δ)-trans Sasakian manifold Bulletin of the Transilvania University of Brasov Series III: Mathematics, Informatics, Physics, 13 (62), 1, 2020, 247-260. [13] Xufeng, U. and Xiaoli, C. Two theorems on e -Sasakian manifolds , Int. J. Math. Math. Sci., 21 (2) (1998), 249-254. | ||
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