Trans-Sasakian Manifolds Homothetic to Sasakian Manifolds

被引：29

作者：

Deshmukh, Sharief ^{[1
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2016年 / 13卷 / 05期

关键词：

Almost contact metric manifold; Sasakian manifold; trans-Sasakian manifold; Poisson equation;

D O I：

10.1007/s00009-015-0666-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, it is shown that for a 3-dimensional compact simply connected trans-Sasakian manifold of type , the smooth functions satisfy the Poisson equations , and , respectively, if and only if it is homothetic to a Sasakian manifold. We also find a necessary and sufficient condition for a connected 3-dimensional trans-Sasakian manifold of type in terms of a differential equation satisfied by the smooth function to be homothetic to a Sasakian manifold.

引用

页码：2951 / 2958

页数：8

共 15 条

[1]

[Anonymous], 1964, Tohoku Math. J.

[2]

[Anonymous], 2008, Extracta Math.

[3]

Blair D.E., 1990, Publications Matematiques, V34, P199

[4]

Blair DE., 1976, Contact manifolds in Riemannian geometry

[5]

De U. C., 2003, Kyungpook Mathematical Journal, V43, P247

[6] Curvature bounds for the spectrum of a compact Riemannian manifold of constant scalar curvature [J].

Deshmukh, S ;

Al-Eid, A .

JOURNAL OF GEOMETRIC ANALYSIS, 2005, 15 (04) :589-606

[7] A note on trans-Sasakian manifolds [J].

Deshmukh, Sharief ;

Tripathi, Mukut Mani .

MATHEMATICA SLOVACA, 2013, 63 (06) :1361-1370

[8]

FUJIMOTO A, 1974, TENSOR, V28, P43

[9]

Gray A., 1980, Annali di Matematica Pura ed Applicata, V123, P35, DOI [DOI 10.1007/BF01796539, 10.1007/BF01796539]

[10]

Kenmotsu K., 1972, TOHOKU MATH J, V24, P93

← 1 2 →