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(ϵ)-Kenmotsu manifold admitting Schouten-van Kampen connection

S. Girish Babu, R. Rajendra, P. Siva Kota Reddy, N. Pavani

Abstract

The objective of this paper is to study some properties of quasi-conformal and concircular tensor on (ϵ)-Kenmotsu manifold admitting the Schouten-van Kampen connection. Expressions of the curvature tensor, Ricci tensor and scalar curvature admitting Schouten-van Kampen connection have been obtained. Locally symmetric -Kenmotsu manifold admitting Schouten-van Kampen connection and quasicon formally flat as well as quasi-conformally semisymmetric -Kenmotsu manifolds admitting Schouten-van Kampen connection are studied.


Keywords

(ϵ)-Kenmotsu manifold; quasi-conformal curvature tensor; concircular curvature tensor; Schouten-van Kampen connection

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References

1. De UC, Sarkar A. On (ϵ)-Kenmotsu manifold. Hadronic Journal 2009; 32(2): 231–242.

2. Bejancu A, Farran HR. Foliations and Geometric Structures. Springer; 2006.

3. Ianus S. Some almost product structures on manifolds with linear connection. Kodai Mathematical Seminar Reports 1971; 23(3): 305–310. doi: 10.2996/kmj/1138846369

4. Schouten JA, van Kampen ER. On the embedding and curvature theory of nonholonomic entitie (German) Mathematische Annalen 1930; 103: 752–783. doi: 10.1007/BF01455718

5. Olszak Z. The Schouten-van Kampen affine connection adapted to an almost (para) contact metric structure. arXiv 2013; arXiv:1402.5796. doi: 10.2298/PIM1308031O

6. Ghosh G. On Schouten-van Kampen connection in Sasakian manifolds. Boletim da Sociedade Paranaense de Matematica 2018; 36(4): 171–182. doi: 10.5269/bspm.v36i4.33105

7. Yildiz A. f-Kenmotsu manifolds with the Schouten–van Kampen connection. Publications de L’institut Mathématique 2017; 102(116): 93–105. doi: 10.2298/PIM1716093Y

8. Alghamdi MA, Bahadir O. Some characterizations in Kenmotsu manifolds with a new connection. arXiv 2020; arXiv:1804.10020. doi: 10.48550/arXiv.1804.10020

9. Angadi PG, Shivaprasanna GS, Somashekhara G, Reddy PSK. Ricci-Yamabe solitons on submanifolds of some indefinite almost contact manifolds. Advances in Mathematics: Scientific Journal 2020; 9(11): 10067–10080. doi: 10.37418/amsj.9.11

10. Angadi PG, Shivaprasanna GS, Somashekhara G, Reddy PSK. Ricci solitons on (LCS)-manifolds under D-homothetic deformation. Italian Journal of Pure & Applied Mathematics 2021; 46: 672–683.

11. Angadi PG, Reddy PSK, Shivaprasanna GS, Somashekhara G. On weakly symmetric generalized (k, µ)-space forms. Proceedings of the Jangjeon Mathematical Society 2022; 25(2): 133–144.

12. Mert T, Atceken M, Uygun P. Semi-symmetric generalized Sasakian space forms on some special curvature tensors. Konuralp Journal of Mathematics 2022; 10(2): 240–249.

13. Mert T, Atceken M, Uygun P. Semi-symmetric almost C(α)-manifold on some curvature tensors. Gulf Journal of Mathematics 2023; 14(2): 101–114. doi: 10.56947/gjom.v14i2.1179

14. Mert T, Atceken M, Uygun P. Normal paracontact metric space form on w_0- curvature tensor. Journal of Amasya University the Institute of Sciences and Technology 2023; 4(1): 53–64. doi: 10.54559/jauist.1312242

15. Murthy BP, Naveen Kumar RT, Reddy PSK, Venkatesha. On N(k)-contact metric manifold endowed with pseudo-quasi-conformal curvature tensor. Advances in Mathematics: Scientific Journal 2021; 10(4): 1969–1982. doi: 10.37418/amsj.10.4.11

16. Murthy BP, Naveen Kumar RT, Reddy PSK, Venkatesha. Extended Pseudo projective curvature tensor on (LCS)n-manifold. Proceedings of the Jangjeon Mathematical Society 2022; 25(3): 347–354.

17. Nagaraja HG, Kumari D, Reddy PSK. Submanifold of (κ,μ)- contact metric manifold as a Ricci soliton. Proceedings of the Jangjeon Mathematical Society 2021; 24(1): 11–19. doi: 10.17777/pjms2021.24.1.11

18. Naveen Kumar RT, Reddy PSK, Venkatesha, Alloush KAA. (LCS)n-manifold endowed with torse forming vector field and concircular curvature tensor. International Journal of Mathematical Combinatorics 2022; 3: 38–47.

19. Siddiqi MD, Bahadir O. η-Ricci solitons on Kenmotsu manifold with generalized symmetric metric connection. arXiv 2018; arXiv:1809.00485. doi: 10.22190/FUMI2002295S

20. Somashekhara G, Pavani N, Reddy PSK. Invariant sub-manifolds of LP-Sasakian manifolds with semi-symmetric connection. Bulletin of Mathematical Analysis and Applications 2020; 12(2): 35–44.

21. Somashekhara G, Babu SG, Reddy PSK. C-Bochner curvature tensor under D-homothetic deformation in LP-Sasakian manifold. Bulletin of the International Mathematical Virtual Institute 2021; 11(1): 91–98.doi: 10.7251/BIMVI2101091S

22. Somashekhara G, Babu SG, Reddy PSK. Indefinite Sasakian manifold with quarter-symmetric metric connection. Proceedings of the Jangjeon Mathematical Society 2021; 24(1): 91–98.

23. Somashekhara G, Reddy PSK, Pavani N, Manjula GJ. η-Ricci-Yamabe solitons on submanifolds of some indefinite almost contact manifolds. Journal of Mathematical and Computational Science 2021; 11(3): 3775–3791.

24. Somashekhara G, Babu SG, Reddy PSK. Conformal Ricci soliton in an indefinite trans-Sasakian manifold. Vladikavkaz Mathematical Journal 2021; 23(3): 45–51. doi: 10.46698/t3715-2700-6661-v

25. Somashekhara G, Babu GS, Reddy PSK. Ricci solitons and generalized weak symmetries under D-homothetically deformed LP-Sasakian manifolds. Italian Journal of Pure & Applied Mathematics 2021; (46): 684–695.

26. Somashekhara G, Babu SG, Reddy PSK. Conformal η-Ricci solitons in Lorentzian para-Sasakian manifold admitting semisymmetric metric connection. Italian Journal of Pure & Applied Mathematics 2021; 46: 1008–1019.

27. Somashekhara G, Reddy PSK, Shivashankara, Pavani N. Slant sub-manifolds of generalized Sasakian-space-forms. Proceedings of the Jangjeon Mathematical Society 2022; 25(1): 83–88.

28. Somashekhara G, Reddy PSK, Pavani N. Semi-invariant submanifolds of generalized Sasakian-space-forms. International Journal of Mathematical Combinatorics 2022; 2: 47–55.

29. Somashekhara G, Babu SG, Reddy PSK, Shivashankara. On LP-Sasakian manifolds admitting generalized symmetric metric connection. Proceedings of the Jangjeon Mathematical Society 2022; 25(3): 287–296.

30. Somashekhara G, Rajendra R, Shivaprasanna GS, et al. Generalised Sasakian-space-form in submanifolds. International Journal of Mathematical Combinatorics 2022; 3: 69–81.

31. Somashekhara G, Babu SG, Reddy PSK. η-Ricci solitonin an indefinite trans-Sasakian manifold admitting semi-symmetric metric connection. Boletim da SociedadeParanaense de Matemática 2023; 41: 1–9. doi: 10.5269/bspm.51358

32. Somashekhara G, Rajendra R, Shivaprasanna GS, Reddy PSK. Pseudo parallel and generalized Ricci pseudo parallel invariant submanifolds of a generalized Sasakian space form. Proceedings of the Jangjeon Mathematical Society 2023; 26(1): 69–78.

33. Somashekhara P, Naveen Kumar RT, Reddy PSK, et al. Pseudo projective curvature tensor on generalized Sasakian space forms. Proceedings of the Jangjeon Mathematical Society 2023; 26(3): 243–251.

34. Yano K, Sawaki S. Riemannian manifolds admitting a conformal transformation group. Journal of Differential Geometry 1968; 2(2): 161–184.

35. Yano K. Concircular geometry. I. Concircular transformations. Proceedings of the Imperial Academy Tokyo 1940; 16(6): 195–200. doi: 10.3792/pia/1195579139


DOI: https://doi.org/10.59400/jam.v1i2.113
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