Complete lift of a tensor field of type (1,2) to semi-cotangent bundle

Abstract

The main purpose of this paper is to define the complete lift of a projectable tensor field of type (1,2) to semi-cotangent bundle t*M. Using projectable geometric objects on M, we examine lifting problem of projectable tensor field of type (1,2) to the semi-cotangent bundle. We also present the good square in the semi-cotangent bundle t*M.

Keywords

• Complete lift,pull-back bundle,semi-cotangent bundle

References

1. K. Yano and S. Ishihara, Tangent and Cotangent Bundles. Marcel Dekker, Inc., New York, 1973.
2. D. Husemoller, Fibre Bundles. Springer, New York, 1994.
3. H. B. Lawson and M.L. Michelsohn, Spin Geometry. Princeton University Press., Princeton, 1989.
4. N. Steenrod, The Topology of Fibre Bundles. Princeton University Press., Princeton, 1951.
5. F. Yıldırım, On a special class of semi-cotangent bundle, Proceedings of the Institute of Mathematics and Mechanics, (ANAS) 41 (2015), no. 1, 25-38.
6. F. Yıldırım and A. Salimov, Semi-cotangent bundle and problems of lifts, Turk J. Math, (2014), 38, 325-339.
7. L. S. Pontryagin, Characteristic cycles on differentiable manifolds. Rec. Math. (Mat. Sbornik) N.S., 21 (63):2, (1947), 233-284.
8. W. A. Poor, Differential Geometric Structures, New York, McGraw-Hill (1981).

9. N. M. Ostianu, Step-fibred spaces, Tr. Geom. Sem. 5, Moscow. (VINITI), 259-309 (1974).
10. V. V. Vishnevskii, Integrable affinor structures and their plural interpretations. Geometry, 7.J. Math. Sci. (New York) 108 (2002), no. 2, 151-187.
11. F. Etayo, The geometry of good squares of vector bundles, Riv. Mat. Univ. Parma 17 (1991) 131-147.