A New Class of Contact Pseudo Framed Manifolds with Applications
In this paper, we introduce a new class of contact pseudo framed (CPF)-manifolds M,g,f,λ,ξ by a real tensor field f of type 1,1, a real function λ such that f3=λ2f where ξ is its characteristic vector field. We prove in our main Theorem 2 that M admits a closed 2-form Ω if λ is constant. In 1976, Bl...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2021/6141587 |
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| Summary: | In this paper, we introduce a new class of contact pseudo framed (CPF)-manifolds M,g,f,λ,ξ by a real tensor field f of type 1,1, a real function λ such that f3=λ2f where ξ is its characteristic vector field. We prove in our main Theorem 2 that M admits a closed 2-form Ω if λ is constant. In 1976, Blair proved that the vector field ξ of a normal contact manifold is Killing. Contrary to this, we have shown in Theorem 2 that, in general, ξ of a normal CPF-manifold is non-Killing. We also have established a link of CPF-hypersurfaces with curvature, affine, conformal collineations symmetries, and almost Ricci soliton manifolds, supported by three applications. Contrary to the odd-dimensional contact manifolds, we construct several examples of even- and odd-dimensional semi-Riemannian and lightlike CPF-manifolds and propose two problems for further consideration. |
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| ISSN: | 0161-1712 1687-0425 |