TY - JOUR T1 - Some characterizations of hyperbolic Ricci solitons on nearly cosymplectic manifolds with respect to the Tanaka-Webster connection AU - Altunbaş, Murat PY - 2024 DA - June Y2 - 2024 DO - 10.26650/ijmath.2024.00012 JF - Istanbul Journal of Mathematics PB - Istanbul University WT - DergiPark SN - 2980-3020 SP - 28 EP - 32 VL - 2 IS - 1 LA - en AB - It is known that a hyperbolic Ricci soliton is one of the generalization of the Ricci solitons and it is a Riemannian manifold (𝑀, 𝑔) furnished with a differentiable vector field π‘ˆ on 𝑀 and two real numbers πœ† and πœ‡ ensuring 𝑅𝑖𝑐 + πœ†πΏπ‘ˆπ‘” + 1 2 πΏπ‘ˆ (πΏπ‘ˆπ‘”) = πœ‡π‘”, where πΏπ‘ˆ denotes the Lie derivative with respect to the vector field 𝑋 on 𝑀. Furthermore, hyperbolic Ricci solitons yield similar solutions to hyperbolic Ricci flow. In this paper, we study hyperbolic Ricci solitons on nearly cosymplectic manifolds endowed with the Tanaka-Webster connection. We give some results for these manifolds when the potential vector field is a pointwise collinear with the Reeb vector field and a concircular vector field. KW - hyperbolic Ricci soliton KW - nearly cosymplectic manifold KW - Tanaka KW - Webster connection CR - Ayar, G., 2022, Some curvature tensor relations on nearly cosymplectic manifolds with Tanaka-Webster connection, Universal Journal of Mathematics, 5(1), 24-31. google scholar CR - Azami, S., Fasihi, G., 2023, Hyperbolic Ricci solitons on warped product manifolds, Filomat, 37(20), 6843-6853. google scholar CR - Azami, S., Fasihi, G., Some characterizations of alpha-cosymplectic manifolds admitting hyperbolic Ricci solitons, 2024, preprint (10.13140/RG.2.2.35608.20480) google scholar CR - Blaga, A., Γ–zgΓΌr, C., 2023, Results of hyperbolic Ricci solitons, Symmetry, 15(8), 1548. google scholar CR - Blair, D., 1976, Contact manifolds in Riemannian geometry, Lecture Notes in Math., 509, Springer-Verlag, Berlin. google scholar CR - Faraji, H., Azami, S., Fasihi, G., 2023, Three dimensional homogenous hyperbolic Ricci solitons, Journal of Non-linear Mathematical Physics, 30(1), 135-155. google scholar CR - Kong, D., Liu, K., 2007, Wave character of metrics and hyperbolic flow, J. Math. Phys., 48, 1-14. google scholar CR - Nicola, A., Dileo, G., Yudin, I., 2018, On Nearly Sasakian and Nearly Cosymplectic Manifolds, Annali di Mat. 197(1), 127-138. google scholar CR - Tanno, S., 1969, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. Journal, 21, 21-38. google scholar UR - https://doi.org/10.26650/ijmath.2024.00012 L1 - https://dergipark.org.tr/en/download/article-file/4112061 ER -