Shashikant Pandey, Abhishek Singh, Vishnu Narayan Mishra

DOI Number
First page
Last page


The objective of present research article is to investigate the geometric properties of $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds. In this manner, we consider $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds satisfying $R\cdot S=0$. Further, we obtain results for $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds with quasi-conformally flat property. Moreover, we get results for $\eta$-Ricci solitons in Lorentzian para-Kenmotsu manifolds admitting Codazzi type of Ricci tensor and cyclic parallel Ricci tensor, $\eta$-quasi-conformally semi-symmetric, $\eta$-Ricci symmetric and quasi-conformally Ricci semi-symmetric. At last, we construct an example of a such manifold which justify the existence of proper $\eta$-Ricci solitons.


eta-Ricci solitons; Lorentzian Para-Kenmotsu manifolds; Codazzi type of Ricci tensor; Cyclic parallel Ricci tensor; quasi-conformal curvature tensor.

Full Text:



A. Bejancu and H. Faran: Foliations and geometric structure. Math. and Its

Appl. 580, Springer, Dordrecht, 2006.

B. Cappelletti-Montano, I. Kupeli Erken and C.Murathan: Nullity conditions

in paracontact geometry. Di_. Geom. Appl. 30 (2012), 665-693.

R. S. Hamilton: The Ricci ow on surfaces. Mathematics and General Relativity

(Santa Cruz, CA, 1986), Contemp. Math. 71 (1988), 237-262.

S. Ianus: Some almost product structures on manifolds with linear connection.

Kodai Math. Sem. Rep. 23 (1971), 305-310.

S. Kaneyuki and F. L. Williams: Almost paracontact and parahodge structures

on manifolds. Nagoya Math. J. 99 (1985), 173-187.

K. Mandal and U. C. De: Paracontact metric (k; _)-spaces satisfying certain

curvature conditions. Kyungpook Math. J. 59 (2019), 163-174.

V. A. Mirzoyan: Structure theorems on Riemannian Ricci semisymmetric

spaces. Izv. Vyssh. Uchebn. Zaved. Mat. 6 (1992), 80-89, (in Russian).

Z. Olszak: The Schouten-van Kampen a_ne connection adapted an almost

(para) contact metric structure. Publ. De L'inst. Math. 94 (2013), 31-42.

G. Perelman: The entopy formula for the Ricci ow and its geometric applications.

J. Schouten and E. van Kampen: Zur Einbettungs-und Krummungsthorie

nichtholonomer Gebilde. Math. Ann. 103 (1930), 752-783.

R. Sharma: Certain results on K-contact and $(k; mu)$-contact manifolds. Journal

of Geometry 89 (2008), 138-147.

A. F. Solov'ev: On the curvature of the connection induced on a hyperdistribution

in a Riemannian space. Geom. Sb. 19 (1978), 12-23, (in Russian).

A. F. Solov'ev: The bending of hyperdistributions. Geom. Sb. 20 (1979), 101-

, (in Russian).

A. F. Solov'ev: Second fundamental form of a distribution. Mat. Zametki 35

(1982), 139-146.

A. F. Solov'ev: Curvature of a distribution. Mat. Zametki 35 (1984), 111-124.

Z. Szabo: Structure theorems on Riemannian spaces satisfying R(X,Y).R=0, The

local version. J. Di_erential Geometry 17 (1982), 531-582.

A. Yildiz and U. C. De: A classi_cation of (k; _)-contact metric manifolds.

Commun Korean Math. Soc. 27 (2012), 327-339.

A. Yildiz and U. C. De: Certain semisymmetry curvature conditions on paracontact

metric (k; _)-manifolds. Math. Sci. App. E-Notes 8(1) (2020), 1-10.

S. Zamkovoy: Canonical connections on paracontact manifolds. Ann. Glob. Anal.

Geom. 36 (2009), 37-60.

S. Zamkovoy and V. Tzanov: Non-existence of at paracontact metric structures

in dimension greater than or equal to _ve. Annuaire Univ. So_a Fac. Math.

Inform. 100 (2011), 27-34.



  • There are currently no refbacks.

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