Title: Kenmotsu manifolds with quarter-symmetric non-metric connections
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-21-00060; Volume 5 / Issue 1 / Year 2023, Pages 78-89
Document Type: Research Paper
aDepartment of Applied Science and Humanities, United Collage of Engineering & Research, A-31, UPSIDC Industrial Area, Naini-211010, Prayagraj, India
bDepartment of Mathematics, Wollo University, Dessie, P.O. Box: 1145, South Wollo, Amhara Region, Ethiopia
Received: 2 October 2021, Accepted: 19 June 2023, Published: 29 July 2023
Corresponding Author: Sunil Kumar Yadav (Email address: firstname.lastname@example.org)
Full Text: PDF
We categories Kenmotsu manifold with quarter-symmetric non-metric connections. In relation to this relationship, we examine Ricci soliton on such manifolds. A last example is shown.
Keywords: Ricci soliton, Kenmotsu manifold, quarter-symmetric non-metric connection (𝒬𝒮𝒩ℳ𝒞)References:
- C. L. Bejanb and M. Crasmareanu, Ricci Solitons in manifolds with quasi-constant curvature, Publ. Math. Debrecen 78 (1), 235–243, 2011.
- T. Q. Binh, L. Tamassy, U. C. De and M. Tarafdar, Some remarks on almost Kenmotsu manifolds, Math. Pannon. (N. S.) 13, 31–39, 2002.
- A. M. Blaga, η-Ricci solitons on para-kenmotsu manifolds, Balkan J. Geom. Appl. 20 (1), 1–13, 2015.
- D. E. Blair, Contact manifold in Riemannian geometry, Lecture Notes in Mathematics (LNM, vol. 509), Springer Berlin, Heidelberg, 1976.
- W. M. Boothby and H. C. Wang, On contact manifolds, Ann. of Math. 68 (3), 421–450, 1958.
- B.-Y. Chen and S. Deshmukh, Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl. 19 (1), 13–21, 2014.
- U. C. De, On ϕ-symmetric Kenmotsu manifolds, Int. Electron. J. Geom. 1 (1), 33–38, 2008.
- U. C. De and G. Pathak, On 3-dimensional Kenmotsu manifolds, Indian J. Pure Appl. Math. 35, 159–165, 2004.
- U. C. De, A. Yildiz and F. Yaliniz, On ϕ-recurrent Kenmotsu manifolds, Turkish J. Math. 33 (1), 17–25, 2009.
- R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (2), 255–306, 1982.
- R. S. Hamilton, The Ricci flow on surfaces, mathematics and general relativity, Contemp. Math. 71, 237–262, 1988; https://doi.org/10.1090/conm/071/954419.
- S. K. Hui, S. K. Yadav and A. Patra, Almost conformal Ricci solitons on f-Kenmotsu manifolds, Khayyam J. Math. 1 (5), 84–104, 2019.
- J. B. Jun, U. C. De and G.Pathak, On Kenmotsu manifolds, J. Korean Math. Soc. 42, 435–445, 2005.
- K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24, 93–103, 1972.
- C. Ozgur, On weakly symmetric Kenmotsu manifolds, Differ. Geom. Dyn. Syt. 8, 204–209, 2006.
- C. Ozgur, On generalized recurrent Kenmotsu manifolds, World Appl. Sci. J. 2, 29–33, 2007.
- C. Ozgur and U. C. De, On the quasi-conformal curvature tensor of a Kenmotsu manifolds, Math. Pannon. (N. S.) 17 (2), 221–228, 2006.
- C. Patra and A. Bhattacharyya, Quarter symmetric non-metric connection in on Pseudosymmetric Kenmotsu manifolds, Bull. TICMI 17 (2), 1–14, 2013.
- G. Pitis, A remarks on Kenmotsu manifolds, Bull. Univ. Brasov, Ser. C 30, 31–32, 1988.
- G. P. Pokhariyal, S. K. Yadav and S. K. Chaubey, Ricci solitons on trans-Sasakian manifolds, Differ. Geom. Dyn. Syst. 20, 138–158, 2018.
- G. Prerelman, The entropy formula for the Ricci flow and its geometric applications, ArXiv 2002; http://arXiv.org/abs/math/0211159.
- G. Prerelman, Ricci flow with surgery on three manifolds, ArXiv 2003; http://arXiv.org/abs/math/0303109.
- S. Sasaki and Y. Hatakeyama, On differentiable manifolds with certain structures which are closely related to almost contact structure, Tohoku Math. J. 13, 281–294, 1961.
- R. Sharma, Certain results on k-contact and (k, μ)-contact manifolds, J. Geom. 89, 138–147, 2008.
- T. Takahashi, Sasakian ϕ-symmetric spaces, Tohoku Math. J. 29, 91–113, 1977.
- S. Tano, The automorphism groups of almost contact Riemannian mnaifolds, Tohoku Math. J. 21, 21–38, 1969.
- S. K. Yadav, Ricci solitons on para-Kähler manifolds, Extracta Math. 34 (2), 255–268, 2019.
- S. K. Yadav, S. K. Chaubey and R. Prasad, Kenmotsu manifold admitting semi symmetric metric connections, Facta Univ. Ser. Math. Inform. 35 (1), 101–119, 2020.
- S. K. Yadav and H. Ozturk, On (ϵ)-almost paracontact metric manifolds with conformal η-Ricci solitons, Differ. Geom. Dyn. Syst. 21, 202–215, 2019.
- S. K. Yadav and H. Ozturk, Some results for Ricci and Yamabe soliton on almost Kenmotsu manifolds, Novi Sad J. Math. 2022; https://doi.org/10.30755/NSJOM.13375.
- K. Yano, Integral formulas in Riemannian geometry, Marcel Dekker, Inc., New York, 1970.
- K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics, World Scientific Publishing Co., Springer, 1984.