The Zamkovoy canonical paracontact connection on a para-Kenmotsu manifold

  • D. G. Prakasha Department of Mathematics, Davangere University, Davangere - 577 007, India.
  • H. Harish Department of Mathematics, Mahaveera College, Mudbidri, India – Department of Mathematics, Karnatak University, Dharwad - 580 003, India.
  • P. Veeresha Department of Mathematics, CHRIST (Deemed to be University), Bengaluru - 560029, India.
  • Venkatesha Department of Mathematics, Kuvempu University, Shankaraghatta - 577 4511, Shimoga District, India.
Keywords: Para-Kenmotsu manifold, Zamkovoy canonical paracontact connection, local φ-symmetry, local φ-Ricci symmetry, recurrent, η-Einstein 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.

Published
2021-08-01
How to Cite
[1]
D. G. Prakasha, H. Harish, P. Veeresha, and Venkatesha, “The Zamkovoy canonical paracontact connection on a para-Kenmotsu manifold”, CUBO, vol. 23, no. 2, pp. 191–206, Aug. 2021.
Section
Articles