A New Class of Contact Pseudo Framed Manifolds with Applications

K. L. Duggal and Luca Vitagliano

International Journal of Mathematics and Mathematical Sciences, 2021, vol. 2021, 1-9

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:6141587

DOI: 10.1155/2021/6141587

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