A NOTE ON KENMOTSU MANIFOLDS ADMITTING GENERALIZED TANAKA-WEBSTER CONNECTION

Year 2022, Volume: 5 Issue: 2, 122 - 128, 31.07.2022

Mustafa Yıldırım , Ramazan Çınar Kaya

https://doi.org/10.33773/jum.1134765

Abstract

In the present paper, we investigate some tensor conditions of Kenmotsu manifolds with the generalized Tanaka-Webster connection. Using
the Q tensor whose trace is the well-known Z-tensor, we prove the conditions ξ − Q∗ flat, ϕ − Q∗ flat Kenmotsu manifold with respect to the generalized Tanaka-Webster connection.

Keywords

Kenmotsu manifold, generalized Tanaka-Webster connection, Q tensor

References

• [1] C.A. Mantica, Y.J. Suh, Pseudo Q−symmetric Riemannian manifolds. Int. J. Geom. Methods Mod. Phys. vol.10, pp.1-25, (2013).
• [2] C.A. Mantica, L.G. Molinari, Riemann compatible tensors. Colloq. Math.vol.128 No.2, pp.197-200, (2012).
• [3] B.H. Yilmaz, Sasakian manifolds satisfying certain conditions Q tensor, Journal of Geometry, vol.111, pp.1-10, (2020).
• [4] M. Yıldırım, A new type characterizarion of Kenmotsu manifolds with respect to Q tensor, Journal of Geometry and Physics, vol.176, pp.104498, (2022).
• [5] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J., vol.24, pp.93-103, (1972).
• [6] G.Pitis, Geometry of Kenmotsu Manifolds: Publishing House of Transilvania University of Bra¸sov, Bra¸sov, (2007).
• [7] H. ¨ Ozturk, N. Aktan,C. Murathan, On α−Kenmotsu manifolds satisfying certain conditions, Applied sciences vol.12 , pp.115-126, (2010).
• [8] N. Aktan, On non-existence of lightlike of indefinite Kenmotsu space form, Turkish journal of Math., vol.32 no.2, 127-139, (2008).
• [9] N. Aktan, S. Balkan, M. Yıldırım, On weak symmetries of almost Kenmotsu (κ, μ, ν)-spaces, Hacettepe Journal of Mathematics and Statistics, vol.42 no.4, pp.447-453,(2013).
• [10] G. Ayar, M. Yıldırım, η−Ricci Solitons on nearly Kenmotsu manifolds, Asian-Eur. J. Math., vol.12 no.6,pp. 2040002,(2019).
• [11] M. Yıldırım, On Non-Existence of Weakly Symmetric Nearly Kenmotsu Manifold with Semisymmetric Metric Connection, Konuralp Journal of Mathematics, vol.9 no.2, pp. 332-336, (2021).
• [12] N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan. J. Math. New series, 2 (1976), 131–190.
• [13] S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differ. Geom. 13 (1978), 25–41.
• [14] S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 n. 1 (1989), 349–379.
• [15] Blair, D.E.: Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics , Springer-Verlag, Berlin,(1976)
• [16] Kıran Kumar, D. L., Nagaraja, H. G. ve Kumari, D., 2019. Concircular curvature tensor of Kenmotsu Manifolds admitting generalized Tanaka-Webster connection, J. Math. Comput. Sci., 9, 4, 447-462.
• [17] Tanno, S.: The automorphism groups of almost contact Riemannian manifolds. Tohoku Math, J., 21,21-38, (1969)
• [18] G. Ghosh and U. C. De, Kenmotsu manifolds with generalized Tanaka-Webster connection, Publications de l’Institut Mathematique-Beograd, 102 (2017), 221–230.