Quarter-symmetric metric connection on a p-Kenmotsu manifold





In the present paper we study para-Kenmotsu (p-Kenmotsu) manifold equipped with quarter-symmetric metric connection and discuss certain derivation conditions.


Para-Kenmotsu manifold , quarter-symmetric metric connection , curvature tensor , η- Einstein manifold.

Mathematics Subject Classification:

53C15 , 53C25
  • Pages: 153–166
  • Date Published: 2024-04-10
  • Vol. 26 No. 1 (2024)

S. C. Biswas and U. C. De, “Quarter-symmetric metric connection in an SP-Sasakian manifold,” Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 46, no. 1-2, pp. 49–56, 1997.

A. De, “On Kenmotsu manifold,” Bull. Math. Anal. Appl., vol. 2, no. 3, pp. 1–6, 2010.

U. C. De and G. Pathak, “On 3-dimensional Kenmotsu manifolds,” Indian J. Pure Appl. Math., vol. 35, no. 2, pp. 159–165, 2004.

U. C. De and J. Sengupta, “Quater-symmetric metric connection on a Sasakian manifold,” Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 49, no. 1-2, pp. 7–13, 2000.

U. C. De, D. Mandal, and K. Mandal, “Some characterizations of Kenmotsu manifolds admitting a quarter-symmetric metric connection,” Bull. Transilv. Univ. Braşov Ser. III, vol. 9(58), no. 1, pp. 39–52, 2016.

A. Friedman and J. A. Schouten,“Über die Geometrie der halbsymmetrischen Übertragungen,” Math Z, vol. 21, pp. 211–223, 1924, doi: 10.1007/BF01187468.

S. Gołąb, “On semi-symmetric and quarter-symmetric linear connections,” Tensor (N.S.), vol. 29, no. 3, pp. 249–254, 1975.

A. Haseeb and R. Prasad, “Certain results on Lorentzian para-Kenmotsu manifolds,” Bol. Soc. Parana. Mat. (3), vol. 39, no. 3, pp. 201–220, 2021.

J.-B. Jun, U. C. De, and G. Pathak, “On Kenmotsu manifolds,” J. Korean Math. Soc., vol. 42, no. 3, pp. 435–445, 2005, doi: 10.4134/JKMS.2005.42.3.435.

K. Kenmotsu, “A class of almost contact Riemannian manifolds,” Tohoku Math. J. (2), vol. 24, pp. 93–103, 1972, doi: 10.2748/tmj/1178241594.

M. Kon and K. Yano, Structures on manifolds, ser. Series in Pure Mathematics. Chandrama Prakashan, Allahabad, 1985, vol. 3, doi: 10.1142/0067.

R. S. Mishra, Structures on a differentiable manifold and their applications. Chandrama Prakashan, Allahabad, 1984.

I. Sato, “On a structure similar to the almost contact structure,” Tensor (N.S.), vol. 30, no. 3, pp. 219–224, 1976.

T. Satyanarayana and K. L. S. Prasad, “On a type of para-Kenmotsu manifold,” Pure Mathematical Sciences, vol. 2, no. 4, pp. 165–170, 2013.

R. N. Singh, S. K. Pandey, and G. Pandey, “On a type of Kenmotsu manifold,” Bull. Math. Anal. Appl., vol. 4, no. 1, pp. 117–132, 2012.

B. B. Sinha and K. L. Sai Prasad, “A class of almost para contact metric manifold,” Bull. Calcutta Math. Soc., vol. 87, no. 4, pp. 307–312, 1995.

S. Sular, C. Özgür, and U. C. De, “Quarter-symmetric metric connection in a Kenmotsu manifold,” SUT J. Math., vol. 44, no. 2, pp. 297–306, 2008.

W. Tang, P. Majhi, P. Zhao, and U. C. De, “Legendre curves on 3-dimensional Kenmotsu manifolds admitting semisymmetric metric connection,” Filomat, vol. 32, no. 10, pp. 3651– 3656, 2018, doi: 10.2298/fil1810651t.

M. M. Tripathi, “On a semi symmetric metric connection in a Kenmotsu manifold,” J. Pure Math., vol. 16, pp. 67–71, 1999.

  • Department of Science and Technology (IF200486)


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How to Cite

B. Chaube and S. K. Chanyal, “Quarter-symmetric metric connection on a p-Kenmotsu manifold”, CUBO, vol. 26, no. 1, pp. 153–166, Apr. 2024.