Journal of the Iranian Mathematical Society

Journal of the Iranian Mathematical Society

A generalization of normal almost contact manifolds

Document Type : Research Article

Authors
F. Malek 1
A. Ghoujaei Bavil Oliaei 2
1 Faculty of‎ ‎Mathematics, K‎. ‎N‎. ‎Toosi University of Technology, Tehran‎, ‎Iran.
2 Department of Mathematics, Payam Noor University Tehran, Iran.
10.30504/jims.2024.435257.1158
Abstract
In this article‎, ‎a new definition‎, ‎called $ \varphi $-normal‎, ‎is introduced‎, ‎which is a generalization of normal condition on almost contact manifolds‎. ‎Then some examples of $ \varphi $-normal almost contact manifolds that are not normal are presented‎, ‎and a sufficient and necessary condition for equivalence of these two definitions in 3-dimensional almost contact manifolds is provided‎. ‎In the end‎, ‎it is proven that a $ \varphi$-normal contact metric manifold is a Sasakian manifold‎.
Keywords
‎Sasakian manifolds‎
‎Nijenhuis torsion‎
‎normal almost contact manifolds
Subjects
[1] D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Second edition, Progress in Mathematics, 203, Birkhäuser Boston, Ltd., Boston, MA, 2010.
[2] H. Geiges, Normal contact structures on 3-manifolds, Tohoku Math. J. (2) 49 (1997), no. 3, 415--422.
[3] J. W. Gray, Some global properties of contact structures, Ann. of Math. (2) 69 (1959) 421--450.
[4] A. Newlander, and L. Nirenberg, Complex analytic coordinates in almost complex manifolds, Ann. of Math. 65 (1957) 391--404.
[5] S. Sasaki, On differentiable manifolds with certain structures which are closely related to almost contact structure I, Tohoku Math. J. (2) (1960) 459--476.
[6] S. Sasaki and C. J. Hsu, On a property of Brieskorn manifolds, Tohoku Math. J. (2) 28 (1976), no. 1, 67--78.
[7] S. Sasaki and Y. Hatakeyama, On differentiable manifolds with certain structures which are closely related to almost contact structures II, Tohoku Math. J. (2) 13 (1961) 281--294.
[8] H. Sato, Remarks concerning contact manifolds, Tohoku Math. J. 29 (1977), no. 4, 577--584.
Journal of the Iranian Mathematical Society
Volume 5, Issue 2
March 2024
Pages 233-241