Critical point equation on almost f-cosymplectic manifolds
- Title
- Critical point equation on almost f-cosymplectic manifolds
- Creator
- Kumara H.A.; Venkatesha V.; Naik D.M.
- Description
- Purpose: Besse first conjectured that the solution of the critical point equation (CPE) must be Einstein. The CPE conjecture on some other types of Riemannian manifolds, for instance, odd-dimensional Riemannian manifolds has considered by many geometers. Hence, it deserves special attention to consider the CPE on a certain class of almost contact metric manifolds. In this direction, the authors considered CPE on almost f-cosymplectic manifolds. Design/methodology/approach: The paper opted the tensor calculus on manifolds to find the solution of the CPE. Findings: In this paper, in particular, the authors obtained that a connected f-cosymplectic manifold satisfying CPE with \lambda=\tilde{f} is Einstein. Next, the authors find that a three dimensional almost f-cosymplectic manifold satisfying the CPE is either Einstein or its scalar curvature vanishes identically if its Ricci tensor is pseudo anti?commuting. Originality/value: The paper proved that the CPE conjecture is true for almost f-cosymplectic manifolds. 2021, H. Aruna Kumara, V. Venkatesha and Devaraja Mallesha Naik.
- Source
- Arab Journal of Mathematical Sciences, Vol-29, No. 2, pp. 134-144.
- Date
- 2023-01-01
- Publisher
- Emerald Publishing
- Subject
- Almost f-cosymplectic manifold; Cosymplectic manifold; Critical point equation; Einstein manifold
- Coverage
- Kumara H.A., Department of Mathematics, Kuvempu University, Shimoga, India; Venkatesha V., Department of Mathematics, Kuvempu University, Shimoga, India; Naik D.M., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India
- Rights
- All Open Access; Gold Open Access
- Relation
- ISSN: 13195166
- Format
- Online
- Language
- English
- Type
- Article
Collection
Citation
Kumara H.A.; Venkatesha V.; Naik D.M., “Critical point equation on almost f-cosymplectic manifolds,” CHRIST (Deemed To Be University) Institutional Repository, accessed March 3, 2025, https://archives.christuniversity.in/items/show/14162.