Kyungpook Mathematical Journal

  • 제60권1호
  • /
  • Pages.177-183
  • /
  • 2020
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

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)
  • 투고 : 2019.03.21
  • 심사 : 2019.06.25
  • 발행 : 2020.03.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

  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. https://doi.org/10.1007/PL00005857
  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. https://doi.org/10.1007/s10114-004-0520-2
  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. https://doi.org/10.1007/s00526-008-0221-2
  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. https://doi.org/10.2298/FIL1715695W