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On special weakly M - projective symmetric manifolds | ||
| Journal of Finsler Geometry and its Applications | ||
| دوره 5، شماره 2، 2024، صفحه 48-54 اصل مقاله (268.71 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22098/jfga.2024.14963.1126 | ||
| نویسندگان | ||
| Shyam Kishor؛ Anoop Kumar Verma* | ||
| Department of Mathematics and Astronomy, University of Lucknow, Lucknow, Uttar Pradesh, INDIA | ||
| چکیده | ||
| The notion of a weakly symmetric and weakly projective symmetric Riemannian manifolds has been introduced by Tamassy and Binh and then after studied by so many authors such as De, Shaikh and Jana, Shaikh and Hui, Shaikh, Jana and Eyasmin. Recently, Singh and Khan introduced the notion of Special weakly symmetric Riemannian manifolds and denoted such manifold by (SWS)n. A.U. Khan and Q. Khan found some results On Special Weakly Projective Symmetric Manifolds. And P. Verma and S. Kishor found some results on M-Projective Curvature Tensor on (k, µ)- Contact Space Forms. Motivated from the above, we have studied the nature of Ricci tensor R of type (1,1) in a special weakly M-projective symmetric Riemannian manifold (SWMS)n and also explored some interesting results on (SWMS)n. | ||
| کلیدواژه‌ها | ||
| Keywords: M-projective curvature tensor؛ Curvature Tensor. Ricci tensor؛ Einstein manifold؛ Special weakly M-projective symmetric Riemannian manifold؛ Codazzi type | ||
| مراجع | ||
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1. U.C. De and S. Bandyopadhyay, On weakly symmetric Riemannian spaces, Publ. Math.Debrecen, 54(3-4) (1999), 377-381. 2. Q. Khan, Differential Geometry of manifolds, PHI Learning Private Limited, Delhi110092, (2012). 3. A.A. Shaikh and S.K. Jana, On weakly cyclic Ricci symmetric manifolds, Ann. Polon.Math. 89(3) (2006), 139-146. 4. A.A. Shaikh and S.K. Jana, On weakly symmetric Riemannian manifolds, Publ. Math.Debrecen, 71(1-2) (2007), 27-41. 5. A.A. Shaikh, S.K. Jana and S. Eyasmin, On weakly pseudo quasi-conformally symmetric manifolds, Indian. J of Math. 50(3) (2008), 505-518. 6. A.A. Shaikh and S.K. Hui, On weakly conharmonically symmetric manifolds, Tensor N.S. 70(2) (2008), 119-134. 7. A.A. Shaikh, J. Choi and S.K. Jana, On conformally flat weakly cyclic Ricci symmetric manifolds, Tensor N.S. 70(3) (2008), 241-254. 8. A.A. Shaikh and S.K. Hui, On weakly projective symmetric manifolds, Acta. Math. Acad. Paedagogicae. Nyiregyhaziensis. 25(2) (2009), 247-269. 9. H. Singh and Q. Khan, On symmetric Riemannian manifolds, Novi Sad J. Math.29(3)(1999), 301-308. 10. H. Singh and Q. Khan, On Special weakly symmetric Riemannian manifolds, Publ.Math.. Debrecen. 58(2000), 523-536. 11. L. Tamassy and T.Q. Binh, Weakly symmetric and weakly projective symmetirc Riemannian manifold, Coll. Math. Soc. J. Bolyai. 50(1989), 663-670. 12. L. Tamassy and T.Q. Binh, On weak symmetries of Einstein and Sasakian manifolds,Tensor, N.S. 53(1993), 140-148. 13. A.U. Khan and Q. Khan, On special weakly projective symmetric manifolds, GANITA,71(2) (2021), 73-79. 14. T.Q. Binh, On weakly symmetric Riemannian Spaces, Publ. Math. Debrecen. 42(1993),103-107. 15. M.C. Chaki, On pseudo symmetric manifolds, Ann. St. Univ. Al I Cuza, Iasi. 33(1987),53-58. 16. K. Shyam and V. Pushpendra, Certain results on M-projective curvature tensor on (κ, µ)- contact space forms, Palestine. J of Math. 10(1) (2021), 224-233. 17. K. Shyam and K. Prerna, On M-Projective Curvature Tensor of Generalized SasakianSpace Form, Math. Sci. Lett. 7(1) (2018), 43-47. 18. A. Gray, Einstein-like manifolds which are not Einstein, Geom. Dedicata, 7(1978), 357-280. | ||
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