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Minimal and harmonic Reeb vector fields on trans-Sasakian 3-manifolds

Yaning Wang
대한수학회 (The Korean Mathematical Society)|2018.11|대한수학회지 (Journal of the KMS)|제55권 제6호|pp. 1321-1336

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참고문헌

키워드

trans-Sasakian manifoldminimal vector fieldReeb vector fieldharmonic vector field
주제분류수학

초록

In this paper, we obtain some necessary and sufficient conditions for the Reeb vector field of a trans-Sasakian $3$-manifold to be minimal or harmonic. We construct some examples to illustrate main results. As applications of the above results, we obtain some new characteristic conditions under which a compact trans-Sasakian $3$-manifold is homothetic to either a Sasakian or cosymplectic $3$-manifold.

Abstract

In this paper, we obtain some necessary and sufficient conditions for the Reeb vector field of a trans-Sasakian $3$-manifold to be minimal or harmonic. We construct some examples to illustrate main results. As applications of the above results, we obtain some new characteristic conditions under which a compact trans-Sasakian $3$-manifold is homothetic to either a Sasakian or cosymplectic $3$-manifold.

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