A note on trans-Sasakian manifolds
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In this article, the authors obtained sufficient conditions for a 3D compact trans-Sasakian manifold of type α, β to be homothetic to a cosymplectic manifold.Abstract:
In this paper, we obtain some sufficient conditions for a 3-dimensional compact trans-Sasakian manifold of type (α, β) to be homothetic to a Sasakian manifold. A characterization of a 3-dimensional cosymplectic manifold is also obtained.read more
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Trans-Sasakian Manifolds Homothetic to Sasakian Manifolds
TL;DR: In this paper, it was shown that for a 3D simply connected trans-Sasakian manifold, the smooth functions of the smooth function satisfies the Poisson equations of the manifold's smooth function if and only if it is homothetic to Sasakian manifolds.
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A Note on Compact Trans-Sasakian Manifolds
TL;DR: In this article, necessary and sufficient conditions for a 3D compact and simply connected trans-Sasakian manifold M of type \(α, β) to be homothetic to a Sasakian is given.
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Trans-Sasakian manifolds homothetic to Sasakian manifolds
TL;DR: In this paper, it was shown that for a 3D simply connected trans-Sasakian manifold, the smooth functions satisfy the Poisson equations if and only if it is homothetic to a Sasakian manifolds.
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A Note on Invariant Submanifolds of Trans-Sasakian Manifolds
Chaogui Hu,Yaning Wang +1 more
TL;DR: In this article, necessary and sufficient conditions for an invariant submanifold of a trans-Sasakian manifold to be totally geodesic are given. But these conditions depend on the invariance of the manifold.
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Some Conditions on Trans-Sasakian Manifolds to Be Homothetic to Sasakian Manifolds
TL;DR: In this paper, the authors study 3D compact and connected trans-Sasakian manifold and find necessary and sufficient conditions under which these manifolds are homothetic to Sasakian manifolds.
References
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Book
Contact manifolds in Riemannian geometry
TL;DR: In this paper, the tangent sphere bundle is shown to be a contact manifold, and the contact condition is interpreted in terms of contact condition and k-contact and sasakian structures.
Journal ArticleDOI
The sixteen classes of almost Hermitian manifolds and their linear invariants
Alfred Gray,Luis Hervella +1 more
TL;DR: In this paper, it was shown that sixteen classes of almost Hermitian manifolds can be found in the Euclidean space, and that they are Hermitians in a natural way.
Journal ArticleDOI
A class of almost contact riemannian manifolds
TL;DR: In this article, Tanno has classified connected almost contact Riemannian manifolds whose automorphism groups have themaximum dimension into three classes: (1) homogeneous normal contact manifolds with constant 0-holomorphic sec-tional curvature if the sectional curvature for 2-planes which contain
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The local structure of trans-Sasakian manifolds
TL;DR: In this article, the local structure of trans-Sasakian manifolds of dimension ⩾ 5 has been characterized by giving suitable examples, and the authors give suitable examples for trans-sakian manifold decomposition.