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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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참고문헌 (27)
참고문헌 신청
N. Aktan / 2014 / Almost f-cosymplectic manifolds / Mediterr. J. Math 11(2):775~787
D. E. Blair / 1990 / Conformal and related changes of metric on the product of two almost contact metric manifolds / Publ. Mat 34(1):199~207
X. Chen / 2017 / Notes on Ricci solitons in f-cosymplectic manifolds / Zh. Mat. Fiz. Anal. Geom 13(3):242~253
Uday Chand De / 2012 / ON A CLASS OF THREE-DIMENSIONAL TRANS-SASAKIAN MANIFOLDS / 대한수학회논문집 27(4):795~808
U. C. De / 2008 / On three-dimensional trans-Sasakian manifolds / Extracta Math 23(3):265~277
D. E. Blair / 1990 / Conformal and related changes of metric on the product of two almost contact metric manifolds / Publ. Mat 34(1):199~207
X. Chen / 2017 / Notes on Ricci solitons in f-cosymplectic manifolds / Zh. Mat. Fiz. Anal. Geom 13(3):242~253
Uday Chand De / 2012 / ON A CLASS OF THREE-DIMENSIONAL TRANS-SASAKIAN MANIFOLDS / 대한수학회논문집 27(4):795~808
U. C. De / 2008 / On three-dimensional trans-Sasakian manifolds / Extracta Math 23(3):265~277
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