The decomposition of almost paracontact metric manifolds in eleven classes revisited
- 28 Downloads
This paper is a continuation of our previous work, where eleven basic classes of almost paracontact metric manifolds with respect to the covariant derivative of the structure tensor field were obtained. First we decompose one of the eleven classes into two classes and the basic classes of the considered manifolds become twelve. Also, we determine the classes of \(\alpha \)-para-Sasakian, \(\alpha \)-para-Kenmotsu, normal, paracontact metric, para-Sasakian, K-paracontact and quasi-para-Sasakian manifolds. Moreover, we study 3-dimensional almost paracontact metric manifolds and show that they belong to four basic classes from the considered classification. We define an almost paracontact metric structure on any 3-dimensional Lie group and give concrete examples of Lie groups belonging to each of the four basic classes, characterized by commutators on the corresponding Lie algebras.
KeywordsAlmost paracontact metric manifolds 3-Dimensional almost paracontact manifolds \(\alpha \)-Para-Sasakian manifolds \(\alpha \)-Para-Kenmotsu manifolds
- 1.Alexiev, V., Ganchev, G.: On the classification of almost contact metric manifolds. In: Mathematics and Education in Mathematics, Proceedings of 15th Spring Conference, Sunny Beach, pp. 155–161 (1986)Google Scholar
- 2.Blair, D.E.: Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics, vol. 509. Springer, Berlin (1976)Google Scholar
- 3.Blair, D.E.: Riemannian Geometry of Contact and Symplectic Manifolds. Birkhäuser, Boston (2002)Google Scholar
- 10.Nakova, G., Zamkovoy, S.: Eleven classes of almost paracontact manifolds with semi-Riemannian metric of (n + 1; n). In: Adachi, T., Hashimoto, H., Hristov, M. (eds.) Recent Progress in Diffrential Geometry and its Related Fields, pp. 119–136. World Scientific Publ, Singapore (2012)Google Scholar