Abstract
Let M be an n-dimensional differentiable manifold with an affine connection without torsion and T 11 (M) its (1, 1)-tensor bundle. In this paper, the authors define a new affine connection on T 11 (M) called the intermediate lift connection, which lies somewhere between the complete lift connection and horizontal lift connection. Properties of this intermediate lift connection are studied. Finally, they consider an affine connection induced from this intermediate lift connection on a cross-section σξ(M) of T 11 (M) defined by a (1, 1)-tensor field ξ and present some of its properties.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Davies, E. T., On the curvature of the tangent bundle, Annali di Mat., 181, 1969, 193–204.
Lai, K. F. and Mok, K. P., On the differential geometry of the (1,1) tensor bundle, Tensor (N.S.), 63(1), (2002), 15–27.
Mok, K. P., Metrics and connections on cotangent bundle, Kodai Math. Sem. Rep., 28, 1977, 226–238.
Salimov, A. and Gezer, A., On the geometry of the (1,1)-tensor bundle with Sasaki type metric, Chin. Ann. Math. Ser. B, 32(3), (2011), 369–386.
Salimov, A. A., Gezer, A. and Akbulut, K., Geodesics of Sasakian metrics on tensor bundles, Mediterr. J. Math., 6(2), (2009), 135–147.
Walker, A. G., Connections for parallel distributions in the large, Quart. J. Math. Oxford, 6(2), (1958), 301–308.
Yano, K., Affine connections in an almost product space, Kodai Math. Sem. Rep., 11, 1959, 1–24.
Yano, K. and Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker, Inc., New York, 1973.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Altunbas, M., Gezer, A. On Affine Connections Induced on the (1, 1)-Tensor Bundle. Chin. Ann. Math. Ser. B 39, 683–694 (2018). https://doi.org/10.1007/s11401-018-0089-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11401-018-0089-1