SOME GEOMETRIC PROPERTIES OF PARA-KENMOTSU MANIFOLDS ADMITTING $Q \varphi=\varphi Q$

Rajendra Prasad, Pooja Gupta

DOI Number
https://doi.org/10.22190/FUMI240120008P
First page
095
Last page
111

Abstract


Hereby, some geometric properties such as $\varphi-$ Ricci symmetric, weakly $\varphi$-Ricci symmetric and Ricci-Yamabe soliton as well as parallel 2-form of the para-Kenmotsu manifolds admitting $Q \varphi=\varphi Q$ are discussed. This paper also deals with Ricci-Yamabe soliton on para-Kenmotsu manifold admitting the curvature condition $\mathbf{\widetilde{R}(\xi,\x_1).\s=0}$ and  locally $\varphi-$ Ricci symmetric para-Kenmotsu manifolds of dimension three. Together with we have cited some examples of 3-dimensional $\varphi-$ Ricci symmetric and locally $\varphi-$ Ricci symmetric para-Kenmotsu manifold.

Keywords

Ricci-Yamabe soliton, para-Kenmotsu manifold, Einstein manifold

Full Text:

PDF

References


T. Q. Binh, L. Tamassy, U. C. De and M. Tarafdar: Some Remarks on almost Kenmotsu manifolds, Mathematica Pannonica, 13(2002), 31-39.

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

G. Catino and L. Mazzieri: Gradient Einstein solitons, Nonlinear Anal., 132(2016), 66-94.

P. Dacko: On almost para-cosymplectic manifolds. Tsukuba J. Math., 28, 193–213 (2004).

U. C. De and G. Pathak: On 3-dimensional Kenmotsu manifolds, Indian J. Pure Applied Math., 35(2004), 159-165.

U. C. De and A. Sarkar: On ϕ− Ricci symmetric Sasakian manifolds, Proceedings of the Jangjeon Mathematical Soc., 11(1)(2008), 47-52.

U. C. De: On ϕ−symmetric Kenmotsu manifolds, International Electronic J. Geom., 1(1) (2008), 33-38.

S. G¨uler and M. Crasmareanu: Ricci-Yamabe maps for Riemannian flows and their volume variation and volume entropy, Turk. J. Math., 43 (2019), 2631-2641.

R. S. Hamilton: Lectures on Geometric Flows (Unpublished manuscript, 1989).

R. S. Hamilton: The Ricci Flow on Surfaces, Mathematics and General Relativity (Santa Cruz, CA, 1986), Contemp. Math., A.M.S., 71 (1988), 237-262.

A. Haseeb and R. Prasad: Some results on Lorentzian para-Kenmotsu manifolds, Bull. Transilvanya Univ. of Brasov, 13(62), (2020), 185-198.

S. Kaneyuki and F. L. Williams: Almost para contact and parahodge structures on manifolds, Nagoya Math. J. 99, 173–187(1985).

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

S. Kundu, S. Halder and K. De: On almost ∗- Ricci solitons, Gulf Journal of Mathematics, Vol 13, No. 2 (2022) 33-41.

C. ¨Ozg¨ur and U. C. De: On the quasi-conformal curvature tenor of a Kenmotsu manifold, Mathematica Pannonica, 17(2)(2006), 221-228.

C. ¨Ozg¨ur: On weakly symmetric Kenmotsu manifolds, Differ. Geom. Dyn. Syst., 8(2006), 204-209.

G. Pitis: A remark on Kenmotsu manifolds, Bul. Univ. Brasov, Ser. C, 30 (1988), 31-32.

R. Prasad and S. Kumar: On a class of α−para Kenmotsu manifolds with semisymmetric metric connection, Palestine Journal of Mathematics, 6(2), 297-307(2017).

R. Prasad and S. Kumar: Semi slant Reimannian maps from cosymplectic manifolds into Reimannian manifolds, Gulf Journal of Mathematics, Vol 9, No. 1 (2020) 62-80.

R. Prasad and V. Srivastava: On (ϵ)−Lorentzian para-Sasakian manifolds, Commun. Korean Math. Soc., 27(2), 297-306(2012).

D. G. Prakasha and K. Vikas: On ϕ-recurrent para-Kenmotsu manifolds, Int. J. Pure. Eng. Math. 3(2), 17–26 (2015).

K. L. Sai Prasad and T. Satyanarayana: On para-Kenmotsu manifold, Int. J. Pure Appl. Math. 90(1), 35–41 (2014).

I. Sato: On a structure similar to the almost contact structure, Tensor N.S. 30, 219–224 (1976).

S. S. Shukla and M. K. Shukla: On ϕ-Ricci symmetric Kenmotsu manifolds, Novi Sad J. Math. 39, 2 (2009), 89–95.

B. B. Sinha and K. L. Prasad: A class of almost paracontact metric manifold, Bull. Culcutta Math. Soc. 87, 307–312 (1995).

R. N. Singh, S. K. Pandey and G. Pandey: Second Order parallel tensors on LPSasakian manifolds, Journal of International Academy of Physical Sciences., 13(4), 383-388(2009).

T. Takahashi: Sasakian ϕ−symmetric spaces. Tohoku Math. J., 29(1997), 91-113.

T. Takahashi: Sasakian manifold with pseudo-Riemannian metric, Tohoku Math. J. 21(2), 644–653 (1969).

J. Welyczko: Slant curves in 3-dimensional normal almost paracontact metric manifolds, Mediterr. J. Math. 11(965), (2014). https://doi.org/10.1007/s00009-013-0361-2

S. Zamkovoy: Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36, 37–60 (2009).




DOI: https://doi.org/10.22190/FUMI240120008P

Refbacks

  • There are currently no refbacks.




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