Research Article
Year 2020,
, 351 - 359, 25.06.2020
Abstract
In this paper, we focus on Kenmotsu manifolds. Firstly, we investigate almost quasi Ricci symmetric Kenmotsu manifolds. Then, we study Kenmotsu manifold admitting a Yamabe soliton. We find that if the soliton field of the Yamabe soliton is orthogonal to the characteristic vector field then it is Killing and the manifold has constant scalar curvature. Also, we deal with a Kenmotsu manifold which admits a quasi-Yamabe soliton. Finally, we give an example which verify our results.
Keywords
Kenmotsu manifold Einstein manifold almost quasi Ricci symmetric manifold quasi-yamabe soliton
References
- [1] Sasaki, S., On differentiable manifolds with certain structures which are closely related to almost contact Structure. I., Tohoku Math. J., 2(12) (1960) 459-476.
- [2] Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 2(25) (1972) 93-103.
- [3] Goldberg, S. I., Yano, K. Integrability of almost cosymplectic structures, Pacific J. Math., 31(1969) 373-382.
- [4] Oubina, J. A., New classes of almost contact metric structures, Publ. Math. Debrecen, 32(1985) 187-193.
- [5] Tanno, S., The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J., 2(22) (1969) 21-38.
- [6] Hamilton, R. S., The Ricci flow on surfaces (Mathematics and General Relativity), Contemp. Math., 71(1988) 237-262.
- [7] Hui, S. K., Mandal, Y. C. Yamabe solitons on Kenmotsu manifolds, Commun. Korean Math. Soc., 34(1) (2019) 321-331.
- [8] Karaca, F., Gradient yamabe solitons on multiply warped product manifolds, Int. Electron. J. Geom., 12(2) (2019) 157-168.
- [9] Suh, Y. J., Mandal, K., Yamabe solitons on three-dimensional paracontact metric manifolds, Bull. Iranian Math. Soc., 44(1) (2018) 183-191.
- [10] Blaga, A. M., Some geometrical aspects of Einstein, Ricci and Yamabe Solitons, J. Geom. Symmetry Phys., 52(2019) 17-26.
- [11] Desmukh, S., Chen, B.-Y., A note on Yamabe solitons, Balkan J. Geom. Appl., 23(1) (2018) 37-43.
- [12] Chen, B.-Y., Desmukh, S., Yamabe and quasi-yamabe solitons on Euclidean submanifolds, Mediterr. J. Math., 15(5) (2018) Article 194.
- [13] Blair, D. E., Contact manifolds in Riemannian geometry, Lecture notes in Mathematics, Berlin-Newyork: Springer, 1976.
- [14] Yano, K., Kon, M., Structures on manifolds, Series in Mathematics, World Scientific Publishing: Springer, 1984.
- [15] Kim, J., On almost quasi ricci symmetric manifolds, Commun. Korean Math. Soc., 35(2) (2020) 603-611.
- [16] Yadav, S., Chaubey, K. S., Prasad, R., On Kenmotsu manifolds with a semi-symmetric metric connection, Facta Universitatis (NIS) Ser. Math. Inform., 35(1) (2020) 101-119.
Year 2020,
, 351 - 359, 25.06.2020
Abstract
References
- [1] Sasaki, S., On differentiable manifolds with certain structures which are closely related to almost contact Structure. I., Tohoku Math. J., 2(12) (1960) 459-476.
- [2] Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 2(25) (1972) 93-103.
- [3] Goldberg, S. I., Yano, K. Integrability of almost cosymplectic structures, Pacific J. Math., 31(1969) 373-382.
- [4] Oubina, J. A., New classes of almost contact metric structures, Publ. Math. Debrecen, 32(1985) 187-193.
- [5] Tanno, S., The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J., 2(22) (1969) 21-38.
- [6] Hamilton, R. S., The Ricci flow on surfaces (Mathematics and General Relativity), Contemp. Math., 71(1988) 237-262.
- [7] Hui, S. K., Mandal, Y. C. Yamabe solitons on Kenmotsu manifolds, Commun. Korean Math. Soc., 34(1) (2019) 321-331.
- [8] Karaca, F., Gradient yamabe solitons on multiply warped product manifolds, Int. Electron. J. Geom., 12(2) (2019) 157-168.
- [9] Suh, Y. J., Mandal, K., Yamabe solitons on three-dimensional paracontact metric manifolds, Bull. Iranian Math. Soc., 44(1) (2018) 183-191.
- [10] Blaga, A. M., Some geometrical aspects of Einstein, Ricci and Yamabe Solitons, J. Geom. Symmetry Phys., 52(2019) 17-26.
- [11] Desmukh, S., Chen, B.-Y., A note on Yamabe solitons, Balkan J. Geom. Appl., 23(1) (2018) 37-43.
- [12] Chen, B.-Y., Desmukh, S., Yamabe and quasi-yamabe solitons on Euclidean submanifolds, Mediterr. J. Math., 15(5) (2018) Article 194.
- [13] Blair, D. E., Contact manifolds in Riemannian geometry, Lecture notes in Mathematics, Berlin-Newyork: Springer, 1976.
- [14] Yano, K., Kon, M., Structures on manifolds, Series in Mathematics, World Scientific Publishing: Springer, 1984.
- [15] Kim, J., On almost quasi ricci symmetric manifolds, Commun. Korean Math. Soc., 35(2) (2020) 603-611.
- [16] Yadav, S., Chaubey, K. S., Prasad, R., On Kenmotsu manifolds with a semi-symmetric metric connection, Facta Universitatis (NIS) Ser. Math. Inform., 35(1) (2020) 101-119.
There are 16 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | June 25, 2020 |
| Submission Date | February 19, 2020 |
| Acceptance Date | June 12, 2020 |
| Published in Issue | Year 2020 |