Horizontal lifts of projectable linear connection to semi-tangent bundle

Year 2021, Volume: 50 Issue: 6, 1709 - 1721, 14.12.2021

Furkan Yıldırım

https://doi.org/10.15672/hujms.894782

Abstract

The main aim of this article is to study the horizontal lifts of projectable linear connection in the semi-tangent bundle tM. The properties of complete and horizontal lifts of projectable linear connection for semi-tangent bundle tM are also investigated. Finally, we examine the infinitesimal linear transformation in the semi-tangent bundle with respect to the horizontal lift of a projectable linear connection.

Keywords

Horizontal lift, Projectable linear connection, Pullback bundle, Semi-tangent bundle, Vector field

Supporting Institution

Tübitak

Project Number

(TBAG-3001, MFAG-118F176).

Thanks

The author is supported by the Scientific and Technological Research Council of Turkey (TBAG-3001, MFAG-118F176).

References

• [1] A. Bednarska, On lifts of projectable-projectable classical linear connections to the cotangent bundle, Ann. Univ. Mariae Curie-Skłodowska Sect. A 67 (1), 1-10, 2013.
• [2] N. Cengiz and A.A. Salimov, Complete lifts of derivations to tensor bundles, Bol. Soc. Mat. Mex. 8 (3), 75-82, 2002.
• [3] D. Husemoller, Fibre Bundles, Springer, New York, 1994.
• [4] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Wiley-Inter Sci- ence Publications, New York, 1963.
• [5] H.B. Lawson and M.L. Michelsohn, Spin Geometry, Princeton University Press, Princeton, 1989.
• [6] N.M. Ostianu, Step-fibred spaces, Tr. Geom. Sem. 5, 259-309, 1974.
• [7] L.S. Pontryagin, Characteristic cycles on differentiable manifolds, Amer. Math. Soc. Translation, 32, 1950.
• [8] W.A. Poor, Differential Geometric Structures, New York, McGraw-Hill, 1981.
• [9] A.A. Salimov and E. Kadıoğlu, Lifts of Derivations to the Semitangent Bundle, Turk J. Math. 24, 259-266, 2000.
• [10] N. Steenrod, The Topology of Fibre Bundles. Princeton University Press, Princeton, 1951.
• [11] N. Tanaka, On infinitesimal automorphisms of Siegel domains, Proc. Japan Acad. Ser. A Math. Sci. 45 (5), 335-338, 1969.
• [12] V.V. Vishnevskii, Integrable affinor structures and their plural interpretations, J. Math. Sci. (N.Y.) 108 (2), 151-187, 2002.
• [13] V.V. Vishnevskii, A.P. Shirokov and V.V. Shurygin, Spaces over Algebras, Kazan Gos. Univ. Kazan, 1985 (in Russian).
• [14] K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker, Inc., New York, 1973.
• [15] F. Yıldırım, On a special class of semi-cotangent bundle, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 41 (1), 25-38, 2015.
• [16] F. Yıldırım and A. Salimov, Semi-cotangent bundle and problems of lifts, Turk J. Math. 38, 325-339, 2014.