Warped product spaces with Ricci conditions | Zendy

Sang-Deok Lee | Zendy; Byung Hak Kim | Zendy; Jin Hyuk Choi | Zendy

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Warped product spaces with Ricci conditions

Author(s) -

Sang-Deok Lee,

Byung Hak Kim,

Jin Hyuk Choi

Publication year - 2017

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1606-49

Subject(s) - mathematics , pure mathematics , ricci curvature , ricci flat manifold , manifold (fluid mechanics) , curvature of riemannian manifolds , riemannian manifold , product (mathematics) , soliton , ricci flow , space (punctuation) , mathematical analysis , mathematical physics , scalar curvature , sectional curvature , physics , geometry , computer science , curvature , nonlinear system , mechanical engineering , quantum mechanics , engineering , operating system

In this paper, we study the Ricci soliton in the Riemannian products M = R × B and warped products M = R×f B of the Euclidean space and Riemannian manifolds, and the gradient Ricci soliton in the warped products M = S ×f B of 1-dimensional circle and Riemannian manifolds. Moreover, we introduce the concept of the generalized Ricci soliton and we suggest the method of construction of the Riemannian manifold (M, g) with a Ricci soliton g . Finally, we also study the Lorentzian warped products with the Ricci soliton.

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