Einstein-Weyl structures on trans-Sasakian manifolds
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Xiaomin Chen
Abstract
In this article we study Einstein-Weyl structures on a 3-dimensional trans-Sasakian manifold M of type (α, β). First, we prove that a 3-dimensional trans-Sasakian manifold admitting both Einstein-Weyl structures W± = (g, ±θ) is Einstein, or is homothetic to a Sasakian manifold if α ≠ 0. Next for β ≠ 0 it is proved that M is Einstein, or is homothetic to an f-Kenmotsu manifold if it admits an Einstein-Weyl structure W = (g, κη) for some nonzero constant κ. Finally, a classification is obtained when a trans-Sasakian manifold admits a closed Einstein-Weyl structure. Further, if M is compact we also obtain two corollaries.
The author is supported by Natural Science Foundation of Beijing, China (Grant No.1194025).
Communicated by Július Korbaš
Acknowledgement
The author would like to thank the referee for the comments.
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© 2019 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
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Artikel in diesem Heft
- 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
