∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds
-
Venkatesha
,
Devaraja Mallesha Naik
Abstract
In this paper, we consider *-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if (M, g) is a Kenmotsu manifold and g is a *-Ricci soliton, then soliton constant λ is zero. For 3-dimensional case, if M admits a *-Ricci soliton, then we show that M is of constant sectional curvature –1. Next, we show that if M admits a *-Ricci soliton whose potential vector field is collinear with the characteristic vector field ξ, then M is Einstein and soliton vector field is equal to ξ. Finally, we prove that if g is a gradient almost *-Ricci soliton, then either M is Einstein or the potential vector field is collinear with the characteristic vector field on an open set of M. We verify our result by constructing examples for both *-Ricci soliton and gradient almost *-Ricci soliton.
The second author (D.M.N.) is grateful to University Grants Commission, New Delhi (Ref. No.:20/12/2015(ii)EU-V) for financial support in the form of Junior Research Fellowship.
Communicated by Július Korbaš
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© 2019 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Regular papers
- RNDr. Kvetoslava Dvořáková passed away
- On the Riesz structures of a lattice ordered abelian group
- On Diophantine equation x4 + y4 = n(u4 + v4)
- On a Waring-Goldbach problem involving squares and cubes
- D(n)-quadruples in the ring of integers of ℚ(√2, √3)
- Geometry of ℙ2 blown up at seven points
- Preservation of Rees exact sequences
- Pointwise multipliers between weighted copson and cesàro function spaces
- Some properties associated to a certain class of starlike functions
- Asymptotic properties of noncanonical third order differential equations
- Existence and regularity results for unilateral problems with degenerate coercivity
- Direct and inverse approximation theorems of functions in the Orlicz type spaces 𝓢M
- Some approximation properties of a kind of (p, q)-Phillips operators
- Best proximity points for a new type of set-valued mappings
- Weakly demicompact linear operators and axiomatic measures of weak noncompactness
- Fixed point results for F𝓡-generalized contractive mappings in partial metric spaces
- Einstein-Weyl structures on trans-Sasakian manifolds
- Characterizations of linear Weingarten space-like hypersurface in a locally symmetric Lorentz space
- ∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds
- Uncorrelatedness sets of discrete random variables via Vandermonde-type determinants
- A note on the consistency of wavelet estimators in nonparametric regression model under widely orthant dependent random errors
- On adaptivity of wavelet thresholding estimators with negatively super-additive dependent noise
- Generalized Meir-Keeler type contractions and discontinuity at fixed point II
