Research Article
Year 2016,
Volume: 4 Issue: 4, 276 - 284, 31.12.2016
Abstract
References
- Agashe, S. and Chafle, R., 1992, A semi-symmetric non-metric connection on a Riemannian manifold, Indian Journal Pure Applications, 23, 6, 399-409.
- Bagewadi, C. S. and Ingalahalli, G., 2012, Ricci solitons in α-Sasakain manifolds, ISRN Geometry, 13 p.
- Bejan, C.L. and Crasmareanu, M., 2011, Ricci solitons in manifolds with quasi-constant curvature, Publicationes Mathematicae, Debrecen, 78, 1, 235-243.
- Călin, C. and Crasmareanu, M., 2010, From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds, Bulletin of the Malaysian Mathematical Sciences Society, 33, 3, 361–368.
- Crasmareanu, M., 2012, Parallel tensors and Ricci solitons in N(k)-Quasi Einstein manifolds, Indian Journal of Pure and Applied Mathematics, 43, 4, 359–369.
- De, U. C. and Shaikh, A.A., 2007, Differential geometry of manifolds, Alpha Science International, 298 p.
- Kenmotsu, K., 1972, A class of almost contact Riemannian manifolds, The Tohoku Mathematical Journal, 24, 93–103.
- Liang, K. C., 1972, A nonoscillation theorem for the superlinear case of second order differential equations, SIAM Journal on Applied Mathematics, 23, 4, 456-459.
- Mishra R. S., 1984, Structures on differentiable manifold and their applications, Chandrama Prakasana.
- Nagaraja, H. G. and Premalatha, C. R., 2012, Ricci solitons in Kenmotsu manifolds, Journal of Mathematical Analysis, 3, 2, 18–24.
- Olszak, Z., Rosca, R., 1991, Normal locally conformal almost cosymplectic manifolds, Publicationes Mathematicae Debrecen, 39, 3, 315-323.
- Öztürk, H., Aktan, N. and Murathan, C., 2010, On α-Kenmotsu manifolds satisfying some certain conditions, Applied Sciences, 12, 115-126.
- Prvanovic, M., 1975, On pseudo metric semi-symmetric connections, Publication De L Institut Mathematic Nouvelle Series, 18, 32, 157–164.
- Sengupta, J., De, U. C. and Binh, T. Q., 2000, On a type of semi-symmetric non-metric connection on a Riemannian manifold, Indian Journal of Pure and Applied Mathematics, 31, 1659-1670.
- Sharma, R. and B. B. Sinha, 1983, On para-A-Einstein manifolds, Publications De L’institut Mathematique, 34, 48, 211-215.
- Shukla, S. S. and Singh, D. D., 2010, On (ξ)-Trans-Sasakian manifolds, International Journal of Mathematical Analysis, 4, 49, 2401 - 2414.
- Tripathi, M. M., 2008, Ricci solitons in contact metric manifolds, http://arxiv. org / abs / 0801.4222, 9 p.
- Yıldız, A., De, U. C. and Turan, M., 2013, On 3-dimensional f-Kenmotsu manifolds and Ricci solitons, Ukrainian Mathematical Journal, 65, 5, 620-628.
- Yıldız, A. and Çetinkaya, A., 2013, Kenmotsu manifolds with the semi-symmetric non-metric connection, preprint.
Year 2016,
Volume: 4 Issue: 4, 276 - 284, 31.12.2016
Abstract
In this study, some curvature conditions are given for 3-dimensional f-Kenmotsu manifolds with the semi-symmetric non-metric connection. It is showed that this manifold is not always ξ-projective flat. Moreover, it is informed that if 3-dimensional f-Kenmotsu manifold with the semi-symmetric non-metric connection is Ricci semi-symmetric and regular, then the manifold is an Einstein manifold. Finally, it is proved that 3-dimensional f-Kenmotsu manifold with the semi-symmetric non-metric connection is also an η-Einstein manifold and the Ricci soliton defined on this manifold is named expanding or shrinking with respect to values of f and λ constant.
Keywords
References
- Agashe, S. and Chafle, R., 1992, A semi-symmetric non-metric connection on a Riemannian manifold, Indian Journal Pure Applications, 23, 6, 399-409.
- Bagewadi, C. S. and Ingalahalli, G., 2012, Ricci solitons in α-Sasakain manifolds, ISRN Geometry, 13 p.
- Bejan, C.L. and Crasmareanu, M., 2011, Ricci solitons in manifolds with quasi-constant curvature, Publicationes Mathematicae, Debrecen, 78, 1, 235-243.
- Călin, C. and Crasmareanu, M., 2010, From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds, Bulletin of the Malaysian Mathematical Sciences Society, 33, 3, 361–368.
- Crasmareanu, M., 2012, Parallel tensors and Ricci solitons in N(k)-Quasi Einstein manifolds, Indian Journal of Pure and Applied Mathematics, 43, 4, 359–369.
- De, U. C. and Shaikh, A.A., 2007, Differential geometry of manifolds, Alpha Science International, 298 p.
- Kenmotsu, K., 1972, A class of almost contact Riemannian manifolds, The Tohoku Mathematical Journal, 24, 93–103.
- Liang, K. C., 1972, A nonoscillation theorem for the superlinear case of second order differential equations, SIAM Journal on Applied Mathematics, 23, 4, 456-459.
- Mishra R. S., 1984, Structures on differentiable manifold and their applications, Chandrama Prakasana.
- Nagaraja, H. G. and Premalatha, C. R., 2012, Ricci solitons in Kenmotsu manifolds, Journal of Mathematical Analysis, 3, 2, 18–24.
- Olszak, Z., Rosca, R., 1991, Normal locally conformal almost cosymplectic manifolds, Publicationes Mathematicae Debrecen, 39, 3, 315-323.
- Öztürk, H., Aktan, N. and Murathan, C., 2010, On α-Kenmotsu manifolds satisfying some certain conditions, Applied Sciences, 12, 115-126.
- Prvanovic, M., 1975, On pseudo metric semi-symmetric connections, Publication De L Institut Mathematic Nouvelle Series, 18, 32, 157–164.
- Sengupta, J., De, U. C. and Binh, T. Q., 2000, On a type of semi-symmetric non-metric connection on a Riemannian manifold, Indian Journal of Pure and Applied Mathematics, 31, 1659-1670.
- Sharma, R. and B. B. Sinha, 1983, On para-A-Einstein manifolds, Publications De L’institut Mathematique, 34, 48, 211-215.
- Shukla, S. S. and Singh, D. D., 2010, On (ξ)-Trans-Sasakian manifolds, International Journal of Mathematical Analysis, 4, 49, 2401 - 2414.
- Tripathi, M. M., 2008, Ricci solitons in contact metric manifolds, http://arxiv. org / abs / 0801.4222, 9 p.
- Yıldız, A., De, U. C. and Turan, M., 2013, On 3-dimensional f-Kenmotsu manifolds and Ricci solitons, Ukrainian Mathematical Journal, 65, 5, 620-628.
- Yıldız, A. and Çetinkaya, A., 2013, Kenmotsu manifolds with the semi-symmetric non-metric connection, preprint.
There are 19 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | December 31, 2016 |
| Published in Issue | Year 2016 Volume: 4 Issue: 4 |