Author
K Venu
Bio: K Venu is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 7 citations.
Papers
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01 Aug 2017
TL;DR: In this article, the authors studied the -Ricci solitons in 3-dimensional trans-Sasakian manifolds and showed that they can be computed in 3D.
Abstract: The aim of this paper is to study the -Ricci solitons in 3-dimensionaltrans-Sasakian manifolds
7 citations
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Journal Article•
TL;DR: In this article, it was shown that if a real hypersurface with constant mean curvature of a complex space form satisfying ▽S = 0 and Sξ = ξ for a smooth function, then the structure vector field ξ is principal.
Abstract: We prove that if a real hypersurface with constant mean curvature of a complex space form satisfying ▽S = 0 and Sξ = ξ for a smooth function , then the structure vector field ξ is principal, where S denotes the Ricci tensor of the hypersurface.
9 citations
Posted Content•
TL;DR: Ricci-like solitons with arbitrary potential are introduced and studied on Sasaki-like almost contact B-metric manifolds in this article, where it is proved that the Ricci tensor of such a soliton is the vertical component of both B-means multiplied by a constant, and explicit examples of Lie groups as manifolds of dimensions 3 and 5 equipped with the structures studied are provided.
Abstract: Ricci-like solitons with arbitrary potential are introduced and studied on Sasaki-like almost contact B-metric manifolds. It is proved that the Ricci tensor of such a soliton is the vertical component of both B-metrics multiplied by a constant. It is established that gradient almost Ricci-like solitons have constant soliton coefficients. Explicit examples of Lie groups as manifolds of dimensions 3 and 5 equipped with the structures studied are provided.
6 citations
18 May 2018
TL;DR: In this article, it was shown that a symmetric second order covariant tensor in a δ-Lorentzian Trans Sasakian manifold is a constant multiple of metric ten sor.
Abstract: The object of the present research is to study the δ-Lorentzian Trans Sasakian manifolds addmitting the η-Einstein Solitons and gradient Ein stein soliton. It is shown that a symmetric second order covariant tensor in a δ-Lorentzian Trans Sasakian manifold is a constant multiple of metric ten sor. Also an example of η-Einstein soliton in 3-diemsional δ-Lorentzian Trans Sasakian manifold is provided in the region where δ-Lorentzian Trans Sasakian manifold expanding.
3 citations
26 Dec 2018
TL;DR: In this article, the generalized η-Riccisoliton on trans-Sakian manifolds is studied and it is shown that a trans-sakian manifold which also satisfies the generalized gradient η -Ricci soliton equation satisfiessome conditions, is necessarily Einstein manifold.
Abstract: The object of the present research is to study generalized η-Riccisoliton on trans-Sasakian manifolds. It shows that a trans-Sasakian manifoldwhich also satisfies the generalized gradient η-Ricci soliton equation satisfiessome conditions, is necessarily Einstein manifold.
2 citations
03 Dec 2018
TL;DR: In this article, the existence of Ricci solitons on the (LCS)n-manifolds satisfying certain curvature conditions was studied and it was shown that the Ricci-soliton is a quasi-Einstein soliton.
Abstract: In this paper, we consider an η-Ricci soliton on the (LCS)n-manifolds (M,φ, ξ, η, g) satisfying certain curvature conditions likes: R(ξ,X) · S = 0 and W2(ξ,X) · S = 0. We show that on the (LCS)n-manifolds (M,φ, ξ, η, g), the existence of η-Ricci soliton implies that (M, g) is a quasi-Einstein. Further, we discuss the existence of Ricci solitons with the potential vector field ξ. In the end, we construct the non-trivial examples of η-Ricci solitons on the (LCS)n-manifolds.
2 citations