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

Kübra Karaca; Aydın Gezer; Abdullah Mağden

doi:10.31801/cfsuasmas.987379

Research Article

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

Year 2022, Volume: 71 Issue: 2, 502 - 517, 30.06.2022

Kübra Karaca Aydın Gezer Abdullah Mağden

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

Abstract

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

Keywords

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

References

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.

Year 2022, Volume: 71 Issue: 2, 502 - 517, 30.06.2022

Kübra Karaca Aydın Gezer Abdullah Mağden

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

Abstract

References

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.

There are 12 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	Kübra Karaca 0000-0002-6329-4435 Aydın Gezer 0000-0001-7505-0385 Abdullah Mağden 0000-0002-6025-629X
Publication Date	June 30, 2022
Submission Date	August 26, 2021
Acceptance Date	December 22, 2021
Published in Issue	Year 2022 Volume: 71 Issue: 2

Cite

APA	Karaca, K., Gezer, A., & Mağden, A. (2022). Notes on the second-order tangent bundles with the deformed Sasaki metric. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(2), 502-517. https://doi.org/10.31801/cfsuasmas.987379
AMA	Karaca K, Gezer A, Mağden A. Notes on the second-order tangent bundles with the deformed Sasaki metric. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2022;71(2):502-517. doi:10.31801/cfsuasmas.987379
Chicago	Karaca, Kübra, Aydın Gezer, and Abdullah Mağden. “Notes on the Second-Order Tangent Bundles With the Deformed Sasaki Metric”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 2 (June 2022): 502-17. https://doi.org/10.31801/cfsuasmas.987379.
EndNote	Karaca K, Gezer A, Mağden A (June 1, 2022) Notes on the second-order tangent bundles with the deformed Sasaki metric. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 2 502–517.
IEEE	K. Karaca, A. Gezer, and A. Mağden, “Notes on the second-order tangent bundles with the deformed Sasaki metric”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 2, pp. 502–517, 2022, doi: 10.31801/cfsuasmas.987379.
ISNAD	Karaca, Kübra et al. “Notes on the Second-Order Tangent Bundles With the Deformed Sasaki Metric”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/2 (June 2022), 502-517. https://doi.org/10.31801/cfsuasmas.987379.
JAMA	Karaca K, Gezer A, Mağden A. Notes on the second-order tangent bundles with the deformed Sasaki metric. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:502–517.
MLA	Karaca, Kübra et al. “Notes on the Second-Order Tangent Bundles With the Deformed Sasaki Metric”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 2, 2022, pp. 502-17, doi:10.31801/cfsuasmas.987379.
Vancouver	Karaca K, Gezer A, Mağden A. Notes on the second-order tangent bundles with the deformed Sasaki metric. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(2):502-17.