On the lifts of F_{a}(5,1)-structure on tangent and cotangent bundle

Year 2021, Volume: 70 Issue: 1, 366 - 381, 30.06.2021

Fidan Jabrailzade

https://doi.org/10.31801/cfsuasmas.766788

Abstract

This paper consist of three main sections. In the first part, we obtain the complete lifts of the F_{a}(5,1)-structure on tangent bundle. We have also obtained the integrability conditions by calculating the Nijenhuis tensors of the complete lifts of F_{a}(5,1)-structure. Later we get the conditions of to be the almost holomorfic vector field with respect to the complete lifts of F_{a}(5,1)- structure. Finally, we obtained the results of the Tachibana operator applied to the vector fields with respect to the complete lifts of F_{a}(5,1)-structure on tangent bundle. In the second part, all results obtained in the first section investigated according to the horizontal lifts of F_{a}(5,1)-structure in tangent bundle T(Mⁿ). In finally section, all results obtained in the first and second section were investigated according to the horizontal lifts of the F_{a}(5,1)- structure in cotangent bundle T^{∗}(Mⁿ).

Keywords

Integrability, Tachibana operators, Lifts, Tangent bundle, Cotangent bundle, Sasakian metric

References

• Andreou, F.G., On a structure defined by a tensor field f satisfying f^5+f = 0. Tensor, N.S., 36 (1982), 79-84, 180-184.
• Çayır, H., Some notes on lifts of almost paracontact structures, American Review of Mathematics and Statistics, 3(1) (2015), 52-60.
• Çayır, H., Lie derivatives of almost contact structure and almost paracontact structure with respect to XV and XH on tangent bundle T(M), Proceedings of the Institute of Mathematics and Mechanics, 42(1) (2016), 38-49.
• Çayır, H., Tachibana and Vishnevskii operators applied to XV and XH in almost paracontact structure on tangent bundle T(M), New Trends in Mathematical Sciences, 4(3) (2016), 105-115.
• Çayır, H., Köseoglu, G., Lie derivatives of almost contact structure and almost paracontact structure with respect to XC and XV on tangent bundle T(M), New Trends in Mathematical Sciences, 4(1) (2016), 153-159.
• Goldberg, S.I., Yano, K., Globally framed f-manifolds, Illinois J. Math., 15(1971), 456-476.
• Ishıhara, S., Yano, K., On integrability conditions of a structure f satisfying f^3 + f = 0; Quaterly J. Math., 15(1964), 217-222.
• Kobayashi, S., Nomizu, K., Foundations of Differential Geometry-Volume I. John Wiley & Sons, Inc, New York 1963.
• Mishra, R.S., On almost product and almost decomposable manifolds. Tensor, N.S., 21(1970), 255-260.
• Nivas, R., Prasad, C.S., On a structure defined by a tensor field f of type (1; 1) satisfying f^2K + f^2 = 0. To appear, Analele Universitatea din Timi, soara, Romania.
• Nivas, R., Prasad, C.S., On a structure defined by a tensor field f(≠ 0) of type (1; 1) satisfying f^5 - a^2f = 0. Nep. Math. Sc. Rep., 10(1) (1985), 25-30.
• Salimov, A.A., Tensor Operators and Their applications, Nova Science Publ., New York, 2013.
• Salimov, A.A., Çayır, H., Some notes on almost paracontact structures, Comptes Rendus de 1'Acedemie Bulgare Des Sciences, 66(3) (2013), 331-338.
• Yano, K., On a structure defined by a tensor field f of type (1; 1) satisfying f^3 + f = 0; Tensor, 14(1963), 99-109.
• Yano, K., Patterson., E.M., Vertical and complete lifts from a manifold to its cotangent bundles, Journal Math. Soc. Japan, 19(1967), 91-113.
• Yano, K., Patterson, E.M., Horizontal lifts from a manifold to its cotangent bundle, J. Math. Soc. Japan 19(1967), 185-198.
• Yano,K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker Inc., New York, 1973.