Tbilisi Mathematical Journal

Certain results on para-Kenmotsu manifolds equipped with $M$-projective curvature tensor

Abhishek Singh and Shyam Kishor

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Abstract

The purpose of the article is to study the certain results on para-Kenmotsu manifolds equipped with $M$-projective curvature tensor. Here we investigate para-Kenmotsu manifolds satisfying some curvature conditions $\widetilde{M}\cdot R=0,$ $\widetilde{M}\cdot Q=0$ and $Q\cdot \widetilde{M}=0,$ where $R$, $Q$ and $\widetilde{M}$ respectively denote the Riemannian curvature tensor, Ricci operator and $M$-projective curvature tensor.

Article information

Source
Tbilisi Math. J., Volume 11, Issue 3 (2018), 125-132.

Dates
Received: 8 April 2018
Accepted: 2 May 2018
First available in Project Euclid: 3 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1538532031

Digital Object Identifier
doi:10.32513/tbilisi/1538532031

Mathematical Reviews number (MathSciNet)
MR3954199

Subjects
Primary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C26: Hyper-Kähler and quaternionic Kähler geometry, "special" geometry

Keywords
para-Kenmotsu manifold Ricci operator Riemannian curvature tensor Riemannian manifold

Citation

Singh, Abhishek; Kishor, Shyam. Certain results on para-Kenmotsu manifolds equipped with $M$-projective curvature tensor. Tbilisi Math. J. 11 (2018), no. 3, 125--132. doi:10.32513/tbilisi/1538532031. https://projecteuclid.org/euclid.tbilisi/1538532031


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References

  • T. Adati and K. Matsumoto, On conformally recurrent and conformally symmetric $P$-Sasakian manifolds, TRU Math., 13 (1977), 25-32.
  • A. M. Blaga, $\eta $-Ricci solitons on para-Kenmotsu manifolds, Balkan Journal of Geometry and Its Applications, 20(1) (2015), 1-13.
  • D. E. Blair, Two remarks on contact metric structures, Tohoku Math. J., 29 (1977), 319-324.
  • A. L. Besse, Einstein manifolds, Springer-verlag, Berlin-Heidelberg (1987).
  • S. K. Chaubey and R. H. Ojha, On the $M$ -projective curvature tensor on Kenmotsu manifolds, Diff. Goem. Dynam. Syst., 12 (2010), 52-60.
  • P. Dacko and Z. Olszak, On weakly para-cosymplectic manifolds of dimension 3. J. Geom. Phys. 57 (2007), 561-570.
  • S. Ivanov, D. Vassilev and S. Zamkovoy, Conformal paracontact curvature and the local flatness theorem. Geom. Dedicata 144 (2010), 79-100.
  • U. C. De and S. Samui, $E$-Bochner curvature tensor on $(k, \mu )$-contact metric manifolds, Int. Electron. J. Geom., 7(1) (2014), 143-153.
  • U. C. De and P. Pal, On generalized $M$ -projectively recurrent manifolds, Ann. Univ. Paedagog. Crac. Stud. Math., 13 (2014), 77-101.
  • U. C. De and S. Mallick, $m$-Projective curvature tensor on $N(k)$-quasi-Einstein manifolds, Diff. Geom. Dynam. Syst., 16 (2014), 98-112.
  • U. C. De and A. Haseeb, On generalized Sasakian-space-forms with $M$-projective curvature tensor, Adv. Pure Appl. Math., 9(1) ( 2018), 67–73.
  • R. Deszcz, L. Verstraelen and S. Yaprak, Warped products realizing a certain conditions of pseudosymmetry type imposed on the Weyl curvature tensor, Chin. J. Math. 22 (1994), 139-157.
  • A. Ghosh, T. Koufogiorgos and R. Sharma, Conformally flat contact metric manifolds, J. Geom., 70 (2001), 66-76.
  • K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J., 24 (1972), 93-103.
  • S. Kaneyuki and F. L. Williams, Almost paracontact and parahodge structure on manifolds, Nagoya Math. J., 99 (1985), 173-187.
  • P. Majhi and G. Ghosh, On a classification of Para-Sasakian manifolds, Facta Universitatis, Ser. Math. Inform., 32(5) (2017), 781–788.
  • R. H. Ojha, A note on the $M$-projective curvature tensor, Indian J. Pure Appl. Math., 8 (12) (1975), 1531-1534.
  • R. H. Ojha, $M$-projectively flat Sasakian manifolds, Indian J. Pure Appl. Math., 17(4) (1986), 481-484.
  • G. P. Pokhariyal and R. S. Mishra, Curvature tensor and their relativistic significance II, Yokohama Math. J., 19 (1971), 97-103.
  • K. L. Sai Prasad and T. Satyanarayan, On para-Kenmotsu manifold, Int. J. Pure Appl. Math., 90(1) (2014), 35-41.
  • B. B. Sinha and K. L. Prasad, A class of Almost paracontact metric manifold, Bull. Calcutta Math, Soc., 87 (1995), 307-312.
  • I. Sato, On a structure similar to the almost contact structure I, Tensor N. S., 30 (1976), 219-224.
  • T. Takahashi, Sasakian manifold with pseudo-Riemannian metric, Thoku Math. J., 21(2) (1969), 644-653.
  • K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics, World Scientific Publishing Co., Singapore 3 (1984).
  • J. Welyczko, Slant curves in $3$ -dimensional normal almost paracontact metric manifolds, Mediter, J. Math., (2013).
  • S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36(1) (2009), 37-60.