Parallel tensors and Ricci solitons in N (k)-quasi Einstein manifolds

Crâşmăreanu, Mircea

doi:10.1007/s13226-012-0022-3

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction3

η-Einstein Soliton Equation1

Eta-ricci Soliton On αLpha-sasakian Manifold1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2014

2022

Publication Types

Select...

Article10

Relationship

Self Cite0

Independent10

Authors

Journals

Cited by 23 publications

(16 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An important geometrical object in studying Ricci solitons is a symmetric (0, 2)tensor field which is parallel with respect to the Levi-Civita connection [2], [7]. The existence of such tensors on smooth manifolds carrying different structures such as contact [14], K-contact [15], P -Sasakian [11], α-Sasakian [8] etc.…”

Section: η-Einstein Soliton Equationmentioning

confidence: 99%

On gradient η-Einstein solitons

Blaga¹

2018

Kragujevac J Mathematics

View full text Add to dashboard Cite

show abstract

Section: η-Einstein Soliton Equationmentioning

confidence: 99%

On gradient η-Einstein solitons

Blaga¹

2018

Kragujevac J Mathematics

View full text Add to dashboard Cite

show abstract

“…Following Perelman [15], we know that a Ricci soliton on a compact manifold is a gradient Ricci soliton. Ricci solitons on contact metric manifods, three-dimensional trans-Sasakian manifolds and N (k)-quasi-Einstein manifolds were studied by Ghosh [8], Turan, De, and Yildiz [18] and Crasmareanu [3], respectively. With regard to the studies of Ricci solitons on Kenmotsu manifolds, we refer the reader to De and Matsuyama [4] and Ghosh [7], respectively.…”

Section: Introductionmentioning

confidence: 99%

Gradient Ricci solitons on almost Kenmotsu manifolds

Wang

Chand

Liu

2015

Publ Inst Math (Belgr)

View full text Add to dashboard Cite

If the metric of an almost Kenmotsu manifold with conformal Reeb foliation is a gradient Ricci soliton, then it is an Einstein metric and the Ricci soliton is expanding. Moreover, let (M 2n+1 , φ, ξ, η, g) be an almost Kenmotsu manifold with ξ belonging to the (k, µ) ′-nullity distribution and h = 0. If the metric g of M 2n+1 is a gradient Ricci soliton, then M 2n+1 is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature −4 and a flat n-dimensional manifold, also, the Ricci soliton is expanding with λ = 4n.

show abstract

“…for any X,Y∈T(M). An important geometrical object in studying Ricci solitons is well-known to be a symmetric (0,2)-tensor field which is parallel with respect to the Levi-Civita connection, some of its geometrical properties being described in [3], [4], [18] etc. In the same manner as in [5] we shall state the existence of η-Ricci solitons in our settings.…”

Section: Eta-ricci Soliton On αLpha-sasakian Manifoldmentioning

confidence: 99%