[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2020.60.1.177

The Critical Point Equation on 3-dimensional α-cosymplectic Manifolds

Blaga, Adara M. (Department of Mathematics, West University of Timisoara)
Dey, Chiranjib (Dhamla Jr. High School)

Publication Information

Kyungpook Mathematical Journal / v.60, no.1, 2020 , pp. 177-183 More about this Journal

Abstract

The object of the present paper is to study the critical point equation (CPE) on 3-dimensional α-cosymplectic manifolds. We prove that if a 3-dimensional connected α-cosymplectic manifold satisfies the Miao-Tam critical point equation, then the manifold is of constant sectional curvature -α², provided Dλ ≠ (ξλ)ξ. We also give several interesting corollaries of the main result.

Keywords

critical point equation; 3-dimensional ${\alpha}$ -cosymplectic manifolds;

Citations & Related Records

Reference

1	I. K. Erken, On a classification of almost ${\alpha}$ -cosymplectic manifolds, Khayyam J. Math., 5(2019), 1-10.
2	S. Hwang, Critical points of the total scalar curvature functionals on the space of metrics of constant scalar curvature, Manuscripta Math., 103(2000), 135-142. DOI
3	T. W. Kim and H. K. Pak, Canonical foliations of certain classes of almost contact metric structures, Acta Math. Sin. (Engl. Ser.), 21(4)(2005), 841-846. DOI
4	P. Miao and L.-F. Tam, On the volume functional of compact manifolds with boundary with constant scalar curvature, Calc. Var. Partial Differ. Equ., 36(2009), 141-171. DOI
5	H. Ozturk, N. Aktan and C. Murathan, Almost ${\alpha}$ -cosymplectic ( $k,{\mu},{\upsilon}$ )-spaces, arXiv:1007.0527 [math. DG].
6	H. Ozturk, C. Murathan, N. Aktan and A.Turgut Vanh, Almost ${\alpha}$ -cosymplectic f-manifolds, An. Stiint. Univ. Al. I. Cuza Iasi Mat. (N.S.) 60(1)(2014), 211-226.
7	D. S. Patra and A. Ghosh, Certain contact metric satisfying the Miao-Tam critical condition, Ann. Polon. Math., 116(3)(2016), 263-271.
8	Y. Wang and W. Wang, An Einstein-like metric on almost Kenmotsu manifolds, Filomat, 31(15)(2017), 4695-4702. DOI