The Zamkovoy canonical paracontact connection on a para-Kenmotsu manifold
Abstract
The object of the paper is to study a type of canonical linear connection, called the Zamkovoy canonical paracontact connection on a para-Kenmotsu manifold.
References
A. M. Blaga, “η-Ricci solitons on para-Kenmotsu manifolds”, Balkan J. Geom. Appl., vol. 20, no. 1, pp. 1-13, 2015.
A. M. Blaga, “Canonical connections on para-Kenmotsu manifolds”, Novi Sad J. Math., vol. 45, no. 2, pp. 131-142, 2015.
A. M. Blaga, “Generalized dual connections on para-Kenmotsu manifolds”, Bull. Int. Math. Virtual Inst., vol. 7, no. 1. pp. 165-171, 2017.
A. M. Blaga, “Invariant, anti-invariant and slant submanifolds of a para-Kenmotsu manifold”, Geom. Balkan Press, BSG Proc. vol. 24, pp. 19-28, 2017.
U. C. De and A. Sarkar, “On φ-Ricci symmetric Sasakian manifolds”, Proc. Jangjeon Math. Soc., vol. 11, no. 1, pp. 47-52, 2008.
U. C. De, A. A. Shaikh and S. Biswas, “On φ-recurrent Sasakian manifolds”, Novi Sad J. Math., vol. 33, no. 2, pp. 43-48, 2003.
U. C. De, A. Yildiz and A. F. Yaliniz, “On φ-recurrent Kenmotsu manifolds”, Turk. J. Math., vol. 33, pp. 17-25, 2009.
S. Ghosh and U. C. De, “On φ-Ricci symmetric (κ, μ)-contact metric manifolds”, Acta Math. Univ. Comenian. (N.S.), vol. 86, no. 2 pp. 205-213, 2017.
S. Kaneyuki, F. L. Williams, “Almost paracontact and parahodge structures on manifolds”, Nagoya Math. J., vol. 99, pp. 173-187, 1985.
K. Kenmotsu, “A class of almost contact Riemannian manifolds”, Tohoku Math. J., vol. 24, pp. 93-103, 1972.
E. M. Patterson, “Some theorems on Ricci-recurrent spaces”, journal London Math. Soc., vol. 27, pp. 287-295, 1952.
D. G. Prakasha and K. K. Mirji, “On φ-symmetric N(κ)-paracontact metric manifolds”, J. Math., Vol. 2015, Article ID 728298, 6 pages, 2015.
D. G. Prakasha and K. Vikas, “On φ-recurent para-Kenmotsu manifolds”, Int. J. Pure & Engg. Mathematics, vol. 3, no. II, pp. 17-26, 2015.
D. G. Prakasha and B. S. Hadimani, “On Generalized recurrent para-Kenmotsu manifolds”, Glob. J. Pure Appl. Math., vol 11, no. 2, pp. 1049-1059, 2015.
K. L. Sai Prasad, T. Satyanarayana, “On para-Kenmotsu manifold”, Int. J. Pure Appl. Math., vol. 90, no. 1, pp. 35-41, 2014.
T. Satyanarayana, K. L. Sai Prasad, B. Satyanarayana, “On a class of para Kenmotsu manifolds”, Int. J. Pure Appl. Math., vol. 115, no. 4), pp. 827-834, 2017.
A. A. Shaikh and K. K. Baishya, “On φ-symmetric LP-Sasakian manifolds”, Yokohama Math. J., vol. 52, pp. 97-112, 2005.
A. A. Shaikh, T. Basu and S. Eyasmin, “On locally φ-symmetric (LCS)n-manifolds”, Int. J. Pure Appl. Math., vol. 41, no. 8, pp. 1161-1170, 2007.
S. S. Shukla and M. K. Shukla, “On φ-symmetric para-Sasakian manifolds”, Int. J. Math. Anal., vol. 4, no. 16, pp. 761-769, 2010.
B. B. Sinha, K. L. Sai Prasad, “A class of Almost paracontact metric manifold”, Bull. Calcutta Math. Soc., vol. 87, pp. 307-312, 1995.
T. Takahashi, “Sasakian φ-Symmetric Spaces”, Tohoku Math. J., vol. 29, pp. 91-113, 1977.
S. Tanno, “Variational problems on contact Riemannian manifolds”, Trans. Amer. Math. Soc., vol. 314, no. 1, pp. 349-379, 1989.
J. Welyczko, “Slant curves in 3-dimensional normal almost paracontact metric manifolds”, Mediterr. J. Math., 2013.
K. Yano, “Concircular geometry I, Concircular transformations”, Proc. Imp. Acad. Tokyo, vol. 16, no. 16, pp. 195-200, 1940.
S. Zamkovoy, “Canonical connections on paracontact manifolds”, Ann. Glob. Anal. Geom., vol. 36, no. 1, pp. 37-60, 2009.
S. Zamkovoy, “On para-Kenmotsu manifolds”, Filomat, vol. 32, no. 14, pp. 4971-4980, 2018.
S. Zamkovoy, G. Nakova, “The decomposition of almost paracontact metric manifolds in eleven classes revisited”, J. Geom., vol. 109, no. 18, 23 pages, 2018.

Copyright (c) 2021 D. G. Prakasha et al.

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.