On warped product spaces with a certain Ricci condition
1
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
In this paper, we obtain the criteria that the Riemannian manifold B is Einstein or a gradient Ricci soliton from the information of the second derivative of f in the warped product space R ×f B with gradient Ricci solitons. Moreover, we construct new examples of non- Einstein gradient Ricci soliton spaces with an Einstein or non-Einstein gradient Ricci soliton leaf using our main theorems. Finally we also get analogous criteria for the Lorentzian version.
Abstract
In this paper, we obtain the criteria that the Riemannian manifold B is Einstein or a gradient Ricci soliton from the information of the second derivative of f in the warped product space R ×f B with gradient Ricci solitons. Moreover, we construct new examples of non- Einstein gradient Ricci soliton spaces with an Einstein or non-Einstein gradient Ricci soliton leaf using our main theorems. Finally we also get analogous criteria for the Lorentzian version.
참고문헌 (11)
- A. Besse, "Einstein Manifolds" (1987), Springer-Verlag
- H. D. Cao, "Geometry of Ricci solitons" (2008), Lehigh Univ
- M. Eminenti, "Ricci solitons: the equation point of view", Manuscripta Math, 127(3), pp.345~367 (2008)
- M. Fernandez-Lopez, "A remark on compact Ricci solitons", Math. Ann, 340(4), pp.893~896 (2008)
- R. S. Hamilton, "The Ricci flow on surfaces, Mathematics and general relativity", pp.237~262 (1988), American Math. Soc.
- T. Ivey, "Ricci solitons on compact three-manifolds", Differential Geom. Appl, 3(4), pp.301~307 (1993)
- T. Ivey, "New examples of complete Ricci solitons", Proc. Amer. Math. Soc, 122(1), pp.241~245 (1994)
- B. H. Kim, "Warped products with critical Riemannian metric", Proc. Japan Acad. Ser. A Math. Sci, 71(6), pp.117~118 (1995)
- G. Perelman, "Ricci flow with surgery on three manifolds", ~
- P. Petersen, "On gradient Ricci solitons with symmetry", Proc. Amer. Math. Soc, 137(6), pp.2085~2092 (2009)
- R. Pina, "On solutions of the Ricci curvature equation and the Einstein equation", Israel J. Math, 171, pp.61~76 (2009)