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Einstein-Weyl structures on trans-Sasakian manifolds

In: Mathematica Slovaca, vol. 69, no. 6
Xiaomin Chen
Detaily:
Rok, strany: 2019, 1425 - 1436
Kľúčové slová:
Einstein-Weyl structure; trans-Sasakian manifold; Sasakian manifold; f-Kenmotsu manifold; cosymplectic manifold
O článku:
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 $W\pm=(g,\pmθ)$ is Einstein, or is homothetic to a Sasakian manifold if $α\neq0$. Next for $β\neq0$ 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.
Ako citovať:
ISO 690:
Chen, X. 2019. Einstein-Weyl structures on trans-Sasakian manifolds. In Mathematica Slovaca, vol. 69, no.6, pp. 1425-1436. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0319

APA:
Chen, X. (2019). Einstein-Weyl structures on trans-Sasakian manifolds. Mathematica Slovaca, 69(6), 1425-1436. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0319
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 22. 12. 2019