Generalized Extended $C$-Bochner Curvature Tensor on $(\grave{k},\grave{\mu})$-Contact Metric Manifolds

Year 2024, Volume: 17 Issue: 2, 394 - 401, 27.10.2024

Ahmet Yıldız

https://doi.org/10.36890/iejg.1470495

Abstract

The object of the present paper is to study $(\grave{k},\grave{\mu})$-contact metric manifolds with generalized extended $C$-Bochner curvature tensor.

Keywords

(`k; `μ)-contact metric manifold, Sasakian manifold, C-Bochner curvature tensor, generalized extended C-Bochner curvature tensor.

References

• [1] Blair D. E., On the geometric meaning of the Bochner Tensor, Geom. Dedicata 4, 33-38 (1975).
• [2] Blair D.E., Koufogiorgos T., Papantoniou B. J., Contact metric manifolds satisfying a nullity condition, Israel Journal of Math. 91, 189-214 (1995).
• [3] Blair D.E., Two remarks on contact metric structures, Tôhoku Math. J., 29, 319-324, (1977).
• [4] Bochner S., Curvature and Betti numbers, Ann. of Math. (2) 50, 77-93 (1949).
• [5] Boothby W. M., and Wang H. C., On contact manifolds, Ann. of Math. 68, 721-734 (1958).
• [6] Endo H., On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor, Colloq. Math., Vol.LXII, no.2, 293-297 (1991).
• [7] Hasegawa I. and Nakane T., On Sasakian manifolds with vanishing contact Bochner curvature tensor II, Hokkaido Math. J. 11 , 44-51 (1982).
• [8] Ikawa T. and Kon M., Sasakian manifolds with vanishing contact Bochner curvature tensor and constant scalar curvature, Colloq. Math. 37, 113-122 (1977).
• [9] Matsumoto M. and Chuman G., On the C-Bochner curvature tensor, TRU Math., 5 , 21-30 (1969).
• [10] Papantoniou B. J., Contact Riemannian manifolds satisfying R(ξ,X) · R = 0 and ξ ∈ (`k,`μ)-nullity distribution, Yokohama Math. J., 40, 149-161 (1993).
• [11] Shaikh A. A. and Baishya, K. K., On (`k,`μ)-contact metric manifolds, Diff. Geom.-Dynm. System, 8 , 253-261 (2006).
• [12] Yano K., Differential geometry of anti-invariant submanifolds of a Sasakian manifold, Boll. Un. Mat. Ital., 12 , 279-296 (1975).
• [13] Yano K., Anti-invariant submanifolds of a Sasakian manifold with vanishing contact Bochner curvature tensor, J. Diff. Geom., 12 , 153-170 (1977).