Notes on the second-order tangent bundles with the deformed Sasaki metric

Yıl 2022, Cilt: 71 Sayı: 2, 502 - 517, 30.06.2022

Kübra Karaca , Aydın Gezer , Abdullah Mağden

https://doi.org/10.31801/cfsuasmas.987379

Öz

The paper deals with the second-order tangent bundle $T^{2}M$ with the deformed Sasaki metric $\overline{g}$ over an n−dimensional Riemannian manifold $(M,g)$. We calculate all Riemannian curvature tensor fields of the deformed Sasaki metric $\overline{g}$ and search Einstein property of $T^{2}M$. Also the weakly symmetry properties of the deformed Sasaki metric are presented.

Anahtar Kelimeler

Second-order tangent bundle, deformed Sasaki metric, weakly symmetric, curvature tensor field, lifts

Kaynakça

• Bejan, C. L., Crasmareanu, M., Weakly-symmetry of the Sasakian lifts on tangent bundles, Publ. Math. Debrecen, 83(1-2) (2013), 63-69.
• Binh, T. Q.,Tamassy, L., On recurrence or pseudo-symmetry of the Sasakian metric on the tangent bundle of a Riemannian manifold, Indian J. Pure Appl. Math., 35(4) (2004), 555-560.
• Gezer, A., Magden, A., Geometry of the second-order tangent bundles of Riemannian manifolds, Chin. Ann. Math. Ser. B, 38(4) (2017), 985-998. DOI:10.1007/s11401-017-1107-4.
• De Leon M., Vazquez, E., On the geometry of the tangent bundles of order 2, Analele Universitatii Bucuresti Matematica, 34 (1985), 40-48.
• Djaa, M., Gancarzewicz, J., The geometry of tangent bundles of order r, Boletin Academia, Galega de Ciencias, 4 (1985), 147-165.
• Dodson, C. T. J., Radivoiovici, M. S., Tangent and frame bundles order two, Analele Stiintifice ale Universitatii Al. I. Cuza, 28 (1982), 63-71.
• Ishikawa, S., On Riemannian metrics of tangent bundles of order 2 of Riemannian manifolds, Tensor (N.S.), 34(2) (1980), 173-178.
• Magden, A., Gezer, A., Karaca, K., Some problems concerning with Sasaki metric on the second-order tangent bundles, Int. Electron. J. Geom., 13(2) (2020), 75–86. DOI:10.36890/iejg.750905.
• Morimoto, A., Liftings of tensor fields and connections to tangent bundles of higher order, Nagoya Math. J., 40 (1970), 99-120.
• Tani, M., Tensor fields and connections in cross-sections in the tangent bundles of order 2, Kodai Math. Sem. Rep., 21 (1969), 310-325.
• Yano, K., Ako, M., On certain operators associated with tensor field, Kodai Math. Sem. Rep., 20 (1968), 414-436.
• Yano, K., Ishihara, S., Tangent and Cotangent Bundles: Differential Geometry, Marcel Dekker, Inc., 420 p, New York, 1973.