Quasi-Conformally Flat α - Sasakian Manifold Under Schouten-Van Kampen Connection
DOI:
https://doi.org/10.53573/rhimrj.2025.v12n12.014Keywords:
Schouten-van Kampen Connection, M*-projective tensor, ϕ-pseudo-quasi-conformal tensor, α-Sasakian manifoldsAbstract
This study focuses on pseudo-quasi conformally α-Sasakian manifolds via Schouten-van Kampen connection (in short SK connection). We also investigate ϕ pseudo quasi-conformally flat α-Sasakian manifolds via the SK connection. Subsequently, we investigate a distinctive curvature condition for α-Sasakian manifolds with the SK connection.
References
D.E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Math., Vol 203, Birkhauser, 2002.
D. Chinea and C. Gonzales, A classification of almost contact metric manifolds, Ann. Mat. Pura. Appl. 156(1990), 15-30.
K. Yano and M. Kon, Structures on manifolds, World Sci., Singapore (1984).
D. E. Blair, Contact manifolds in Riemannian Geometry, Lecture notes in Math, 509, Springer Verlag, Berlin-Heidelberg-New York(1976).
A.M. Blaga, Canonical connection on Para Kenmotsu manifold, Novi Sad . J. Math, Vol 45, No.2 (2015) 131-142.
S. S. Devi, K. L. S. Prasad and T. Satyanarayana, Certain curvature connections on Lorentzian para-Kenmotsu manifolds, RT & A 17 (2022), no. 2, 413–421.
J.P. Singh, On m-projectively flat almost pseudo Ricci symmetric manifolds. Acta Math. Univ. Comen., New Ser. 86 (2017), 335–343.
S. K. Chaubey and R. H. Ojha, On the m-projective curvature tensor of a Kenmotsu manifold, Differ. Geom. Dyn. Syst. 12 (2010), 52–60.
A. Sil, Some properties of α-Sasakian manifolds, Palestine J. Math. 6(2) (2017) 327–332.
G. Ingalahalli and C. S. Bagewadi, Ricci solitons in α-Sasakian manifolds, Int. Scholarly Research Notices (ID-421384) 2012(1) (2012) 1–13.
L. Das, Second order parallel tensor on α-Sasakian manifold, Acta Mathematica, Academiae Paedagogicae Nyiregyhaziensis, 23(2007), 65-69.
K. Yano and S. Sawaki, Riemannian manifolds admitting a conformal transmation group, J. Differential Geom., 2, (1968), 161-184.
A. A. Shaikh and S. K. Jana, A pseudo-quasi-conformal curvature tensor on Riemannian manifolds, South East Asian J. Math. Science., 4(2005), 15-20.
D. G. Prakasha, T. R. Shivamurthy and K. K. Mirji, On pseudo-quasi-conformal curvature tensor of P-Sasakian manifolds, Elect. J. Math. Anal. Appl., 5(2), (2017), 147-155.
A. Mandal, M. Mallik, R. Das, G. Saha, E. Hoque and M. Rejuan, Study of η-Einstein soli ton on α-Sasakian manifold admitting Schouten-van Kampen connection, J. Hyperstructures, 13(2)(2024), 284-296.
J. A. Schouten and E. R. Van Kampen, Zur Einbettungs-und Krummungstheorie nichtholonomer Gebilde, Math. Ann., 103 (1930), 752-783.
A. Bejancu, Schouten-van Kampen and Vranceanu connections on Foliated manifolds, Anale Stintifice Ale Universitati. “AL.I.CUZA” IASI, Tomul LII, Mathematica, (2006), 37-60.
G. Vranceanu, Sur quelques points de la theorie des espaces non holonomes, Bull. Fac. St. Cernauti, 5(1931), 177-205.
