The “SOME PROPERTIES OF -KENMOTSU MANIFOLDS WITH QUARTER-SYMMETRIC NON-METRIC CONNECTION”

Authors

  • Sangeeta Gautam Sangeeta Gautam Dr Rammanohar Lohia Avadh University Ayodhya Uttar Pradesh
  • Dr. Abhishek Dr. Ram Manohar Lohia Avadh University
  • Lalit Kumar Gautam Dr. Ram Manohar Lohia Avadh University

Keywords:

()-Kenmotsu manifold, quarter-symmetric non-metric connection, Ricci soliton, Quasi-projectively flat, φ-projectively flat.

Abstract

The objective of this paper is to investigate the -Kenmotsu manifolds with quarter-symmetric non-metric connection. We have investigate an -Kenmotsu manifolds admitting the quarter-symmetric non-metric connections satisfying certain conditions. We have further provided the equivalent conditions for Ricci soliton in an -Kenmotsu manifolds to be shrinking or expanding with the quarter-symmetric non-metric connection. We have also investigated -projectively flat, Quasi-projectively flat and some interesting results. Finally we have given an example of 3-dimensional -Kenmotsu manifolds with respect to quarter-symmetric non-metric connection.

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References

U. C. De, Yidiz and E. Ata,On a type of Lorentzian para-Sasakian manifolds, Math. Reports

(66), 1(2014), 61-67.

U.C.De and A.Sarkar, On є-Kenmotsu manifold, Hadronic J, 32(2009), 231-242.

K.De, A.M.Blaga and U.C.De, ٨-Riccisolitons on є-Kenmotsu manifolds, Palestine Journal of Mathematics, 9(2), (2020), 984-990.

U.C.De and O.Cihan, On the quasi-conformal curvature tensor of a Kenmotsu manifolds,

Mathematica Pannonica, 17(2) (2006), 221-228.

U.C.De and A.Yildiz, Certain curvature conditions on generalized Sasakian space forms, Quaest. Math.38(4) (2015), 495-504.

A.Friedmann and A.Schouten, U¨berdie Geometricderhalb symmetris chenU¨bertragung, Math., Zeitschr.,21(1924), 211-223.

A. Haseeb and R. prasad, ٨-conformaly-Ricci solitons in є-Kenmotsu manifold, Publi. DeL‘Instut Mathematique Nouvelle serie, tome108(122) (2020), 91-102.

A.Haseeb, Some results on projective curvature tensor is an є-Kenmotsu manifolds, Plastine

J.Math6(2017),196-203.

A. Haseeb, M. K. Khan and M. D. Siddiqi, Some more results on an є-Kenmotsu manifold with semi-symmetric metric connection, Acta. Math. Univ. Comenianae, 85(2016), 9-20.

R. S. Hamilton, The Ricci flow on surfaces, mathematics and general relativity, Contemp. Math.71(1988), 237-262 https://doi.org/10.1090/conm/071/954419.

G. Ingalahalli and C. S. Bagewadi, Ricci solitons in Lorentzianα-Sasakian manifolds, Acta Math. Acad. P. N.,28(2012), 59-68.

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

S. Saular, C. Ozgur and U. C. De, Quarter symmetric metric connection in a Kenmotsu manifold, SUT Journal of Mathematics,44(2008), no. 2 ,297-306.

G. P. Singh and Sunil Kumar Srivastava, On Kenmotsu Manifold with quarter symmetricnon-metricφ-connection, International Journal of Pure and Applied Mathematical Sciences, 9(2016),no.1, 67-74.

R.N.Singh, S.K.Pandey, G.Pandey and K.Tiwari, On a semi-symmetric metric connection is an є-Kenmotsu manifold, Commun. Korean Math. Soc.29(2014),331-343.

V. Venkatesha and S.V.Vishnuvardhana, є-Kenmotsu manifolds admitting a semi-symmetric connection, Italian J. Pure Appli. Math.38(2017), 615-623.

K.Yano,On semi-symmetric metric connections, Rev. Roumaine Math. Press Apple.

(1970),1579-1586.

Sunil Kumar Yadav and Daya Lal Suthar, Kenmotsu manifolds with quarter-symmetric non- metric connection, Montes Tauras of Journal Mathematics,44(2008), 1-12 (2023).

A. Yildiz, φ-Kenmotsu manifolds with the Schouten-Van Kampton connection, Publi. Inst. Math. (N. S),102(2017), 93-105.

Published

14-11-2024

How to Cite

Sangeeta Gautam, S. G., Abhishek Singh, & Lalit Kumar Gautam. (2024). The “SOME PROPERTIES OF -KENMOTSU MANIFOLDS WITH QUARTER-SYMMETRIC NON-METRIC CONNECTION”. Communications in Mathematics and Applications, 15(2). Retrieved from https://rgnpublications.com/journals/index.php/cma/article/view/2597

Issue

Vol. 15 No. 2 (2024)

Section

Research Article

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