Mohd Danish Siddiqi, Oğuzhan Bahadır

DOI Number
First page
Last page


The objective of the present paper is to study the $\eta$-Ricci solitons on Kenmotsu manifold with generalized symmetric metric connection of type $(\alpha,\beta)$. There are discussed Ricci and $\eta$-Ricci solitons with generalized symmetric metric connection of type $(\alpha,\beta)$ satisfying the conditions $\bar{R}.\bar{S}=0$, $\bar{S}.\bar{R}=0$, $\bar{W_{2}}.\bar{S}=0$ and $\bar{S}.\bar{W_{2}}=0.$. Finally, we construct an example of Kenmotsu manifold with generalized symmetric metric connection of type $(\alpha,\beta)$ admitting $\eta$-Ricci solitons.


Kenmotsu manifold; Generalized symmetric metric connection; eta-Ricci soliton; Ricci soliton, Einstein manifold.


Kenmotsu manifold, Generalized symmetric metric connection, $\eta$-Ricci soliton, Ricci soliton, Einstein manifold.

Full Text:



N. S. Agashe, M. R. Chafle: A semi symetric non-metric connection in a Riemannian manifold. Indian J. Pure Appl. Math. 23 (1992), 399-409.

A. M. Blaga: η-Ricci solitons on Lorentzian para-Sasakian manifolds. Filomat 30 (2016), no. 2, 489-496.

A. M. Blaga: η-Ricci solitons on para-Kenmotsu manifolds. Balkan J. Geom. Appl., 20 (2015), 1-13.

C. S. Bagewadi, G. Ingalahalli: Ricci Solitons in Lorentzian α-Sasakian Manifolds. Acta Math. Acad. Paedagog. Nyhzi. (N.S.) 28(1) (2012), 59-68.

D. E.Blair: Contact manifolds in Riemannian geometry. Lecture note in Mathematics, 509, Springer-Verlag Berlin-New York, 1976.

J. T. Cho, M. Kimura Ricci solitons and Real hypersurfaces in a complex space form, Tohoku Math.J., 61(2009), 205-212.

O. Chodosh, F. T. H. Fong: Rotational symmetry of conical Kahler-Ricci solitons. arxiv:1304.0277v2.2013,.

M. C. Chaki, R. K. Maity: On quasi Einstein manifolds. Publ. Math. Debrecen 57 (2000), 297-306.

U. C. De, D. Kamilya: Hypersurfaces of Rieamnnian manifold with semi-symmetric non-metric connection. J. Indian Inst. Sci. 75 (1995), 707-710.

A. Friedmann, J. A. Schouten: Uber die Geometric der halbsymmetrischen Uber-tragung. Math. Z. 21 (1924), 211-223.

S.Golab: On semi-symmetric and quarter-symmetric linear connections. Tensor 29 (1975), 249-254.

H. A. Hayden: Subspaces of space with torsion. Proc. London Math. Soc. 34 (1932), 27-50.

A. Haseeb, M. A. Khan, M. D. Siddiqi: Some more Results On ε-Kenmotsu Manifold With a Semi-Symmetric metric connection. Acta Math. Univ. Comenianae, vol.

LXXXV, 1(2016), 9-20.

R. S. Hamilton: The Ricci flow on surfaces. Mathematics and general relativity, (Santa Cruz. CA, 1986), Contemp. Math. 71, Amer. Math. Soc., (1988), 237-262.

J. B. Jun, U. C. De, G. Pathak: On Kenmotsu manifolds. J. Korean Math. Soc. 42 (2005), no. 3, 435-445.

H. Levy: Symmetric tensors of the second order whose covariant derivatives vanish,

Ann. Math. 27(2) (1925), 91-98.

H. G. Nagaraja, C. R. Premalatha: Ricci solitons in Kenmotsu manifolds. J. Math. Anal. 3 (2) (2012), 18-24.

K. Kenmotsu: A class of almost contact Riemannian manifold. Tohoku Math. J., 24 (1972), 93-103.

G. Pathak, U. C. De: On a semi-symmetric connection in a Kenmotsu manifold.

Bull. Calcutta Math. Soc. 94 (2002), no. 4, 319-324.

D. G. Prakasha, B. S. Hadimani: η-Ricci solitons on para-Sasakian manifolds. J.

Geom., DOI 10.1007/s00022-016-0345-z.

G. P. Pokhariyal, R. S. Mishra: The curvature tensors and their relativistic significance. Yokohama Math. J. 18 (1970), 105-108.

R. Sharma: Certain results on K-contact and (k,µ)-contact manifolds. J. Geom., 89(1-2) (2008), 138-147.

A. Sharfuddin, S. I. Hussain: Semi-symmetric metric connections in almost contact manifolds. Tensor (N.S.), 30(1976), 133-139.

B. G. Schmidt: Conditions on a connection to be a metric connection. Commun. Math. Phys. 29 (1973), 55-59.

M. D. Siddiqi, M. Ahmad, J. P. Ojha: CR-submanifolds of a nearly trans-hyperpolic Sasakian manifold with semi-symmetric non metric connection. African. Diaspora J.

Math. (N.S.) 2014, 17 (1), 93–105

M. M. Tripathi: On a semi-symmetric metric connection in a Kenmotsu manifold,

J. Pure Math. 16(1999), 67-71.

M. M. Tripathi, N. Nakkar : On a semi-symmetric non-metric connection in a Kenmotsu manifold. Bull. Cal. Math. Soc. 16 (2001), no.4, 323-330.

M. M. Tripathi: Ricci solitons in contact metric manifolds. arXiv:0801.4222 [math.DG].

K. Yano: On semi-symmetric metric connections. Revue Roumaine De Math. Pures Appl. 15(1970), 1579-1586.

K. Yano, M. Kon: Structures on Manifolds. Series in Pure Math., Vol. 3, World Sci., 1984.



  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)