Abstract
In this paper, we study a class of almost contact manifolds, namely locally conformal almost manifolds. We investigate subclasses of such manifolds and prove that some of them contain the class of bundle-like metric structures. Under some conditions, we prove that the class of conformal changes of almost cosymplectic structures is a subclass of (almost)-cosymplectic structures. Examples are also obtained.
Similar content being viewed by others
References
Aktan, N., Yildirim, M., Murathan, C.: Almost \(f\)-cosymplectic manifolds. Mediterr. J. Math. 11(2), 775–787 (2014)
Bejancu, A., Farran, H.R.: Foliations and Geometric Structures Mathematics and its Applications. Springer, Dordrecht (2006)
Blair, D.E.: Riemannian Geometry of Contact and Symplectic Manifolds. Progress in Mathematics, vol. 203. Birkhäuser, New York (2002)
Chern, S.S., Hamilton, R.S.: On Riemannian metrics adapted to three dimensional contact manifolds. Lect. Note Math. 1111, 279–308 (1985)
Chinea, D., Marrero, J.C.: Conformal changes of almost cosymplectic manifolds. Demonstratio Math. 25(3), 641–656 (1992)
de Len, M., Marrero, J.C.: Compact cosymplectic manifolds of positive constant \(\varphi \)-sectional curvature. Extracta Math. 9(1), 28–31 (1994)
Ghosh, A., Sharma, R., Cho, J.T.: Contact metric manifolds with parallel torsion tensor. Ann. Global Anal. Geom. 34(3), 287–299 (2008)
Goldberg, S.I., Yano, K.: Integrability of almost cosymplectic structures. Pacific J. Math. 31, 373–382 (1969)
Gray, J.W.: Some global properties of contact structures. Ann. Math. 69(2), 421–450 (1959)
Kim, T.W., Pak, H.K.: Canonical foliations of certain classes of almost contact metric structures. Acta Math. Sin. Eng. Ser. Aug. 21(4), 841–846 (2005)
Olszak, Z.: Locally conformal almost cosymplectic manifolds. Colloq. Math. 57(1), 73–87 (1989)
Olszak, Z.: On almost cosymplectic manifolds. Kodai Math. J. 4(2), 239–250 (1981)
Sasaki, S.: On differentiable manifolds with certain structures which are closely related to almost contact structure, I. Tôhoku Math. J. 12(3), 459–476 (1960)
Vaisman, I.: Conformal Changes of Almost Contact Metric Structures. Lecture Notes in Mathematics, vol. 792, pp. 435–443. Springer, Berlin (1980)
Tondeur, P.: Geometry of Foliations. Monographs in Mathematics, vol. 90. Birkhäuser, New York (1997)
Acknowledgments
A. Maloko Mavambou would like to thank the Simons Foundation through the RGSM-Project for financial support. The authors thank the referee for helping them to improve the presentation.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Young Jin Suh.
Rights and permissions
About this article
Cite this article
Massamba, F., Mavambou, A.M. A Class of Locally Conformal Almost Cosymplectic Manifolds. Bull. Malays. Math. Sci. Soc. 41, 545–563 (2018). https://doi.org/10.1007/s40840-016-0309-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40840-016-0309-3