A New Class of Contact Pseudo Framed Manifolds with Applications

K. L. Duggal

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

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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https://doi.org/10.1155/2021/6141587

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jijmms:v:2021:y:2021:i:1:n:6141587

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