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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2021/6141587 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832561351220789248 |
|---|---|
| author | K. L. Duggal |
| author_facet | K. L. Duggal |
| author_sort | K. L. Duggal |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-421be26476f4454ba520e8daa9caa89d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-421be26476f4454ba520e8daa9caa89d2025-02-03T01:25:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252021-01-01202110.1155/2021/61415876141587A New Class of Contact Pseudo Framed Manifolds with ApplicationsK. L. Duggal0Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario N9B3P4, CanadaIn 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.http://dx.doi.org/10.1155/2021/6141587 |
| spellingShingle | K. L. Duggal A New Class of Contact Pseudo Framed Manifolds with Applications International Journal of Mathematics and Mathematical Sciences |
| title | A New Class of Contact Pseudo Framed Manifolds with Applications |
| title_full | A New Class of Contact Pseudo Framed Manifolds with Applications |
| title_fullStr | A New Class of Contact Pseudo Framed Manifolds with Applications |
| title_full_unstemmed | A New Class of Contact Pseudo Framed Manifolds with Applications |
| title_short | A New Class of Contact Pseudo Framed Manifolds with Applications |
| title_sort | new class of contact pseudo framed manifolds with applications |
| url | http://dx.doi.org/10.1155/2021/6141587 |
| work_keys_str_mv | AT klduggal anewclassofcontactpseudoframedmanifoldswithapplications AT klduggal newclassofcontactpseudoframedmanifoldswithapplications |