پیوندهای مفید
آمار
| تعداد نشریات | 31 |
| تعداد شمارهها | 484 |
| تعداد مقالات | 4,286 |
| تعداد مشاهده مقاله | 7,298,695 |
| تعداد دریافت فایل اصل مقاله | 4,896,201 |
Geometric structures on Lorentzian para-Kenmotsu manifolds admitting a semi-symmetric metric connection | ||
| Journal of Finsler Geometry and its Applications | ||
| دوره 7، شماره 1، 2026، صفحه 141-160 اصل مقاله (361.53 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22098/jfga.2025.17998.1173 | ||
| نویسندگان | ||
| Abhinav Verma* ؛ Rajendra Prasad؛ Vindhyachal Singh Yadav | ||
| Department of Mathematics and Astronomy, University of Lucknow, 226007-Lucknow, Uttar Pradesh, India | ||
| چکیده | ||
| In this paper, we study Lorentzian para-Kenmotsu manifolds endowed with a semi-symmetric metric connection and establish necessary and sufficient conditions under which the Ricci tensor is ω-parallel with respect to this connection. These results extend classical notions of Ricci parallelism from Riemannian geometry to a broader non-Riemannian framework. In addition, we examine the behavior of concircular and projective curvature tensors on such manifolds and derive structural identities that highlight the influence of semi-symmetric torsion on fundamental geometric invariants. To support our theoretical developments, we construct an explicit 4-dimensional illustration. The findings deepen the understanding of non-Riemannian geometric structures and suggest potential applications in generalized theories of gravity. | ||
| کلیدواژهها | ||
| Semi-symmetric metric connection؛ ω-parallel Ricci tensor؛ Concircular curvature tensor؛ Projective curvature tensor؛ Codazzi type | ||
| مراجع | ||
|
1. T. Adati and K. Matsumoto, On conformally recurrent and conformally symmetric PSasakian manifolds, TRU Math., 13 (1997), 25{32, . 2. J. K. Beem, P. E. Ehrlich and K. L. Easley Global Lorentzian Geometry, 2nd-ed., MarcelDekker, New York, 1996 3. A. Berman, Concircular curvature tensor of a semi-symmetric metric connection in a Kenmotsu manifold, Thai J. Math., 13(1)(2015), 245{257, . 4. D. E. Blair, Contact manifolds in Riemannian Geometry, Lecture Notes in Math., 509,Springer-Verlag, Berlin, (1976). 5. E. Cartan, ´ Sur une classe remarquable d’espaces de riemannians, Bull. Soc. Math.France, 54(1926), 214{264. 6. E. Cartan, ´ Le¸cons sur la g´eom´etrie des espaces de Riemann, 2nd ed., Gauthier-Villars,Paris, (1946). 7. S. K. Chaubey and S. K. Yadav, Study of Kenmotsu manifolds with semi-symmetric metric connection, Univ. J. Math. Appl., 1(2), (2018), 89{97. 8. A. De and S. Mallick, On !-Einstein and weakly φ-symmetric Lorentzian para-Kenmotsu manifolds, Journal of Geometry, 112 (2021), Article 51. DOI: 10.1007/s00022-021-00599-4. 9. U. C. De, On φ-symmetric Kenmotsu manifolds, Int. Electron. J. Geom., 1(1), (2008),33{38. 10. U. C. De, A. A. Shaikh and S. Biswas, On φ-recurrent Sasakian manifolds, Novi Sad J.Math., 33 (2003), 43{48. 11. U. C. De and A. Sarkar, On φ-Ricci Symmetric Sasakian manifolds, Proc. Jangjeon Math. Soc., 11(1) (2008), 47{52. 12. U. C. De and A. Sarkar, On Lorentzian almost paracontact manifolds studying certain conditions, Southeast Asian Bulletin of Mathematics, 33 (2009), 297{307. 13. U. C. De and A. Saha,On Lorentzian para-Kenmotsu manifolds, Mathematica Slovaca,64(6) (2014), 1439{1456. DOI: 10.2478/s12175-014-0272-0. 14. A. Friedmann and J. A. Schouten,Uber die Geometrie der halbsymmetrischen ¨Ubertragung ¨ , Math. Z., 21(1924)., 211-223. 15. A. Haseeb and R. Prasad, Certain results on Lorentzian para-Kenmotsu manifolds, Bol.Soc. Paran. Mat. (3s.), 39(3) (2021), 201-220. 16. H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc., 34 (1932),27-50. 17. T. Imai, Notes on semi-symmetric metric connections, Tensor N. S., 24(1972), 293-296. 18. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J.,24(1972), 93-103. 19. U. K. Kim, Conformally flat generalized Sasakian-space forms and locally symmetric generalized Sasakian-space forms, Note Mat., 26(2006), 55{67. 20. S. Kishor, S. Mishra and A. K. Verma, Study of W7-curvature tensor on (LPK)n manifolds, J. Finsler Geom. Appl. 7(1) (2026), 31-44. 21. M. Kon, Invariant submanifolds in Sasakian manifolds, Math. Ann., 219(1976), 277-290. 22. K. Matsumoto, On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Nat. Sci.,12(1989), 151-156. 23. I. Mihai, L. Nicolescu and R. Rosca, On Exact 2-Para Sasakian Manifolds, Rend. Circ.Mat. Palermo (2), 68 (1999), 223-236. 24. J. V. Narlikar, General Relativity and Gravitation, Macmillan Co. of India, (1978). 25. R. Osserman, Curvature in the Eighties, Amer. Math. Monthly, 97(8)(1990), 731{756. 26. R. Prasad, A. Verma and V. S. Yadav, Characterizations of the perfect fluid Lorentzianpara Kenmotsu spacetimes, GANITA, 73(2) (2023), 89-104. 27. R. Prasad, A. Verma and V. S. Yadav, Characterization of φ-symmetric Lorentzian para-Kenmotsu manifolds, Facta Univ. Ser. Math. Inform., 38(3) (2023), 635{647. 28. R. Prasad, A. Haseeb, A. Verma and V. S. Yadav, A study of φ-Ricci symmetric LPKenmotsu manifolds, Int. J. Maps Math., 7(1) (2024), 33{44. 29. I. Sato, On a structure similar to almost contact structure, Tensor N. S., 30, (1976). 30. B. B. Sinha and K. L. Sai Prasad, A class of almost para contact metric manifold, Bull.Calcutta Math. Soc., 87 (1995), 307-312. 31. H. Stephani, General Relativity: An Introduction to the Theory of the Gravitational Field, Cambridge Univ. Press, Cambridge, (1982). 32. T. Takahashi, Sasakian φ-symmetric spaces, Tohoku Math. J., 29 (1977), 91{113. 33. K. Yano, Concircular geometry I: Concircular transformation, Proc. Imp. Acad. Japan,16 (1940), 195{200. 34. K. Yano, On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl., 15(1970), 1579{1586. | ||
|
آمار تعداد مشاهده مقاله: 279 تعداد دریافت فایل اصل مقاله: 150 |
||