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A note on -conformally flat contact manifolds.
Uday Chand De,Sudipta Biswas +1 more
- Vol. 29, Iss: 1, pp 51-57
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TLDR
In this article, it was shown that a contact manifold with the structure vector field ξ belonging to the k-nullity distribution is ξ -conformally flat if and only if it is an η-Einstein manifold.Abstract:
We prove that a contact manifold with the structure vector field ξ belonging to the k-nullity distribution is ξ -conformally flat if and only if it is an η-Einstein manifold and we give some applications. 2000 Mathematics Subject Classification: 53C15, 53C25read more
Citations
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-Ricci Solitons on Sasakian 3-Manifolds
TL;DR: In this paper, a Ricci tensor tensor of Codazzi type and cyclic parallel tensor has been considered on Sasakian 3-manifolds with curvature condition Q.R = 0 and conformally flat and φ-Ricci symmetric Ricci solitons.
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On $(N(k),\xi)$-semi-Riemannian manifolds: Semisymmetries
Mukut Mani Tripathi,Punam Gupta +1 more
TL;DR: In this article, it was shown that a semi-Riemannian manifold is always a semisymmetric manifold, which is defined by a tensor tensor of type 1,3.
Concircular curvature tensor on k-contact manifolds
TL;DR: In this article, the authors studied -concircularly at, concircularly concubinally at and concirculularly semisymmetric K-contact manifolds.
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Certain results on N(k)-contact metric manifolds
TL;DR: In this article, the authors consider contact metric manifolds whose characteristic vector field is associated with the $k$-nullity distribution, and obtain several results on the Ricci solitons on these manifolds.
Journal ArticleDOI
Beta-almost Ricci solitons on Sasakian 3-manifolds
Pradip Majhi,Debabrata Kar +1 more
TL;DR: In this article, it was shown that a β-almost Ricci soliton whose potential vector field is a contact vector field on a Sasakian 3-manifold is shrinking, and that this type of soliton is isometric to a sphere of radius √ 7.
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.
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Some remarks on space with a certain contact structure
TL;DR: In this article, the authors studied the problem of finding a (φ, ξ, η, g)-connection in a space with a normal contact structure and proved that the space with such a contact structure is an Einstein space.