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Einstein-Weyl structures on trans-Sasakian manifolds

  • Xiaomin Chen EMAIL logo
Published/Copyright: December 22, 2019
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 69 Issue 6

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.

Keywords: Einstein-Weyl structure; trans-Sasakian manifold; Sasakian manifold; f-Kenmotsu manifold; cosymplectic manifold
MSC 2010: Primary 53C40; Secondary 53C15

The author is supported by Natural Science Foundation of Beijing, China (Grant No.1194025).

  1. Communicated by Július Korbaš

Acknowledgement

The author would like to thank the referee for the comments.

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Received: 2018-11-15
Accepted: 2019-04-07
Published Online: 2019-12-22
Published in Print: 2019-12-18

© 2019 Mathematical Institute Slovak Academy of Sciences

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  7. Geometry of ℙ2 blown up at seven points
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https://doi.org/10.1515/ms-2017-0319
Keywords for this article
Einstein-Weyl structure; trans-Sasakian manifold; Sasakian manifold; f-Kenmotsu manifold; cosymplectic manifold

Articles in the same Issue

  1. Regular papers
  2. RNDr. Kvetoslava Dvořáková passed away
  3. On the Riesz structures of a lattice ordered abelian group
  4. On Diophantine equation x4 + y4 = n(u4 + v4)
  5. On a Waring-Goldbach problem involving squares and cubes
  6. D(n)-quadruples in the ring of integers of ℚ(√2, √3)
  7. Geometry of ℙ2 blown up at seven points
  8. Preservation of Rees exact sequences
  9. Pointwise multipliers between weighted copson and cesàro function spaces
  10. Some properties associated to a certain class of starlike functions
  11. Asymptotic properties of noncanonical third order differential equations
  12. Existence and regularity results for unilateral problems with degenerate coercivity
  13. Direct and inverse approximation theorems of functions in the Orlicz type spaces 𝓢M
  14. Some approximation properties of a kind of (p, q)-Phillips operators
  15. Best proximity points for a new type of set-valued mappings
  16. Weakly demicompact linear operators and axiomatic measures of weak noncompactness
  17. Fixed point results for F𝓡-generalized contractive mappings in partial metric spaces
  18. Einstein-Weyl structures on trans-Sasakian manifolds
  19. Characterizations of linear Weingarten space-like hypersurface in a locally symmetric Lorentz space
  20. ∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds
  21. Uncorrelatedness sets of discrete random variables via Vandermonde-type determinants
  22. A note on the consistency of wavelet estimators in nonparametric regression model under widely orthant dependent random errors
  23. On adaptivity of wavelet thresholding estimators with negatively super-additive dependent noise
  24. Generalized Meir-Keeler type contractions and discontinuity at fixed point II
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