Abstract
References
- [1] A.L. Besse, Einstein Manifolds, Spring-Verlag, Berlin, (1987).
- [2] H.D. Cao, Geometry of Ricci solitons, Chin. Ann. Math. Ser. B, 27(2), (2006), 121-142.
- [3] H.D. Cao, Recent progress on Ricci solitons, arXiv:0908.2006v1.
- [4] B.Y. Chen, Pseudo-Riemannian geometry, d-invariants and applications,World Scientific Publishing Co. Pte. Ltd,Usa, (2011).
- [5] B.Y. Chen, SH. Deshmukh, Ricci solitons and concurrent vector fields, arXiv:1407.2790.
- [6] S. Deshmukh, F.R. Al-Solamy, Conformal vector fields on a Riemannian manifold, Balkan Journal of Geometryand Its Applications, 19(2), (2014), 86-93.
- [7] J.N. Gomes, Q. Wang, C. Xia, On the h-almost Ricci soliton. arXiv:1411.6416v2.
- [8] R.S. Hamilton, Three manifolds with positive Ricci curvature, J. Diff. Geom., 17, (1982),255-306.
- [9] R.S. Hamilton, The Ricci flow on surfaces, Contemporary Mathematics, 71, (1988), 237-261.
- [10] B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press Limited, London,(1983).
- [11] S. Pigola, M. Rigoli, M. Rimoldi, A.G. Setti, Ricci almost solitons, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 10,(2011), 757-799.
- [12] M. Sanchez, Lorentzian manifolds admitting a Killing vector field, Nonlinear Analysis, 30, (1997), 643-654.
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- [14] S. Shenawy B. Unal, 2-Killing vector fields on warped product manifolds, Int. J. Math, 26, (2015), [17 pages].
Abstract
An h-almost Ricci soliton is a generalization of the Ricci soliton. In this paper we study Ricci solitons and h-almost Ricci solitons on twisted (and warped) product manifolds. First, we obtain some results about Ricci solitons on twisted products. Then we generalize them to h- almost Ricci solitons.
Keywords
Ricci soliton h-almost Ricci soliton concurrent vector field twisted product warped product Robertson-Walker space-time
References
- [1] A.L. Besse, Einstein Manifolds, Spring-Verlag, Berlin, (1987).
- [2] H.D. Cao, Geometry of Ricci solitons, Chin. Ann. Math. Ser. B, 27(2), (2006), 121-142.
- [3] H.D. Cao, Recent progress on Ricci solitons, arXiv:0908.2006v1.
- [4] B.Y. Chen, Pseudo-Riemannian geometry, d-invariants and applications,World Scientific Publishing Co. Pte. Ltd,Usa, (2011).
- [5] B.Y. Chen, SH. Deshmukh, Ricci solitons and concurrent vector fields, arXiv:1407.2790.
- [6] S. Deshmukh, F.R. Al-Solamy, Conformal vector fields on a Riemannian manifold, Balkan Journal of Geometryand Its Applications, 19(2), (2014), 86-93.
- [7] J.N. Gomes, Q. Wang, C. Xia, On the h-almost Ricci soliton. arXiv:1411.6416v2.
- [8] R.S. Hamilton, Three manifolds with positive Ricci curvature, J. Diff. Geom., 17, (1982),255-306.
- [9] R.S. Hamilton, The Ricci flow on surfaces, Contemporary Mathematics, 71, (1988), 237-261.
- [10] B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press Limited, London,(1983).
- [11] S. Pigola, M. Rigoli, M. Rimoldi, A.G. Setti, Ricci almost solitons, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 10,(2011), 757-799.
- [12] M. Sanchez, Lorentzian manifolds admitting a Killing vector field, Nonlinear Analysis, 30, (1997), 643-654.
- [13] S. Shenawy, Ricci solitons on warped product manifolds, arXiv:1508.02794.
- [14] S. Shenawy B. Unal, 2-Killing vector fields on warped product manifolds, Int. J. Math, 26, (2015), [17 pages].
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Article |
| Authors | |
| Publication Date | November 30, 2018 |
| IZ | https://izlik.org/JA67ED86MG |
| Published in Issue | Year 2018 Volume: 15 Issue: 2 |