Tran-Sasakian Manifolds homothetic to Sasakian Manifolds

Journal Article

Alsolamy, Sharief Deshmukh, U.C.De and Falleh . 2016

• نوع عمل المنشور: Research Article
• المجلة \ الصحيفة: Publicationes Mathematicae Debrecen
• رقم العدد: 3-4
• رقم الإصدار السنوي: 88
• الصفحات: 439-448

مستخلص المنشور

In this paper, it is shown that for a 3-dimensional compact simply connected trans-Sasakian manifold of type (α, β), the smooth functions α, β satisfy the Poisson equations Δα = β, Δα = α2β and Δβ = α2β, 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 (α, β) in terms of a differential equation satisfied by the smooth function α to be homothetic to a Sasakian manifold