Ricci Solitons on Para-Kenmotsu Manifolds Admitting Schouten-Van-Kampen Connection

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Published: 2026-06-15
Keywords:
Para-Kenmotsu manifolds, Ricci solitons, Schouten-Van-Kampen connection, curvature tensors, Submanifolds

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Giteshwari Pandey
Department of Mathematics and Computer Science, Govt Model Science College, Rewa, M.P., India
Pratima Dubey
Department of Mathematical Sciences, A.P.S. University, Rewa, M.P., India
Shravan K. Pandey
Department of Mathematical Sciences, A.P.S. University, Rewa, M.P., India
R.N. Singh
Department of Mathematical Sciences, A.P.S. University, Rewa, M.P., India

Abstract

In this paper, we study para-Kenmotsu manifolds equipped with the Schouten-Van-Kampen connection in the framework of Ricci so;itons geometry.We begin by analyzing curvature tensor associated with this connection and establish several intrinsic properties of para-kenmotsu manifolds. Ricci solitons compatible with Schouten-van-Kampen connection are then characterized, yielding new geometric insights. furthermore,we investigate specific curvature condition under which such manifolds admit Ricci solitons, with particular attention given to the projective flatness and concurrency of the structure vector field $\xi$. Finally, the existence and behaviour of Ricci solitons on submanifolds of para-Kenmotsu manifolds are examined relative to the Levi-Civita connection and Schouten-Van-Kampen connection respectively. 

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Vol. 30 No. 2 (2026): Table of Content

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Ricci Solitons on Para-Kenmotsu Manifolds Admitting Schouten-Van-Kampen Connection. J. Int. Acad. Phys. Sci. [Internet]. 2026 Jun. 15 [cited 2026 Oct. 23];30(2):81-9. Available from: http://www.iaps.org.in/journal/index.php/journaliaps/article/view/1035

References

T. Takahashi; Sasakian manifolds with Pseudo-Riemannian metric, Thoku Math.J., 21(2) (1969), 644-653.

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

T. Adati and K.Matsumoto; On conformally recurrent and conformally symmetric P-Sasakian manifolds, TRU Math, 13 (1977), 25-32.

U.C. De; On φ-symmetric Kenmotsu manifolds, International Electronic Journal of Geometry, 1 (2008), 33-38.

R.N. Singh, S.K. Pandey and G.Pandey; On a type of Kenmotsu manifolds, Bull. Math. Anal. Appl., 4,(1) (2012), 117-132.

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

J. Welyczko; Slant curves in 3-dimensional normal almost paracontact meric manifolds, Mediter J.Math., 11 (2014). 965-978.

B.B Sinha and K.L. Prasad; A class of almost para contact metric manifolds, Bull. Calcutta Math. Soc., 87 (1995), 307-312.

A.M. Blaga; η- Ricci solitons on para-Kenmotsu manifolds, Balkan Journal of Geometry and its Application, 20(1) (2015), 1-13.

K.L. Sai Prasad and T.Satyanarayan; On para-Kenmotsu manifolds, Int. J. Pure Appl. Math., 90(1) (2014), 35-41.

T. Raghuwanshi, G. Pandey, M.K. Pandey and Anil Goyal; On generalized projective curvature tensor of para-Kenmotsu manifolds, Miskolc Mathematical Notes, 24(1) (2023), 383-394.

A. Sardar and U.C.De; η-Ricci solitons on para-Kenmotsu manifolds, Differ. Geom. Dyn. Syst., 22 (2020), 218-228.

R.S. Hamilton; Three manifolds with positive Ricci curvature, J. Differential Geom., 17(2) (1982), 255-306.

U.C. De and Y. Matsuyama; Ricci solitons and gradient Ricci solitons in a Kenmotsu manifold, Southeast Asian Bull.Math, 37(5) (2013), 691-697.

C.S. Bagewadi and G.Ingalahalli; Ricci solitons in Lorentzian α-Sasakian manifolds, Acta Mathematica Academiae Paedagogicas Nyiregyhaziensis, 28(1) (2012), 59-68.

R.L. Patel, S.K. Pandey and R.N. Singh; Ricci solitons on ϵ-para Sasakian manifolds admitting concircular curvature tensor, International Journal of Engineering and Management Research, 05(7) (2020), 20-25.

S.K. Pandey, R.L. Patel and R.N. Singh; Ricci solitons in an ϵ-Kenmotsu manifolds admitting conharmonic curvature tensor, International Journal on recent and innovation trends in computing and communication, 05(11) (2017), 75-85.

U.C. De and Mandal Krishanu; Ricci solitons and gradient Ricci solitons on N(k)-Paracontact manifolds, Journal of Mathematical Physics, Analysis, Geometry, 15(3) (2019), 307-320.

A.N. Siddiqui, M.D. Siddiqi and Vandana; Ricci Soliton on α - Sasakian manifolds with quarter symmetric metric connection, Bulletin of the Transilvania University of Brasov,Series III: Mathematics and Computer Science, 66(4) (2024), 175-190.

Z. Olszak; The Schouten-Van-Kampen affine connection adapted to an almost(para) contact metric structure, Publications de I`Institut Mathematique, 94 (2013), 31-42.

A.F. Solvev; On the curvature of the connection induced on a hyperdistribution in a Riemannian space, Geometricheskii Sbornik, 19 (1978), 12-23.

A. Bejancu; Schouten-Van-Kampen and Vranceanu connection on Foliated manifoldsL, Anal.Univ.(AI.I.Cuza Tasi Mat.), 52 (2006), 37-60.

Gurupadavva Ingahalli, S.C. Anil and C.S. Bagewadi; Some results of Kenmotsu manifolds admitting Schouten-Van-Kampen connection, Mathlab journal, 7 (2020).

B. Kumhar, G. Pandey, S.K. Mishra, R.N. Singh; ϵ- Kenmotsu manifolds admitting Schouten-Van-Kampen connection, Bull. Cal. Math. Soc., 114(5) (2022), 767-786.