Musical isomorphisms and problems of lifts

Abstract

Using the complete lift on tangent bundles, the authors construct the complete lift on cotangent bundles of tensor fields with the aid of a musical isomorphism. In this new framework, the authors have a new intrepretation of the complete lift of tensor fields on cotangent bundles.

Keywords

Tensor fields / Cotangent bundles / Complete lift / Anti-Hermitian metric / Riemannian extension

References

[1] Bejan C.. Almost para-Hermitian structures on the tangent bundle of an almost para-co-Hermitian manifold. Proceedings of the Fifth National Seminar of Finsler and Lagrange Spaces (Brasov, 1988), 1989, Bucharest: Soc. Stiinte Mat. R. S., Romania 105-109

[2] Cruceanu V.. Une classe de structures géométriques sur le fibré cotangent. International Conference on Differential Geometry and Its Applications (Bucharest, 1992), 1993 196-201

[3] Cruceanu V., Fortuny P., Gadea P. M.. A survey on paracomplex geometry. Rocky Mountain J. Math., 1996, 26(1): 83-115

[4] Druta S. L.. Classes of general natural almost anti-Hermitian structures on the cotangent bundles. Mediterr. J. Math., 2011, 8(2): 161-179

[5] Druta-Romaniuc S. L.. Riemannian almost product and para-Hermitian cotangent bundles of general natural lift type. Acta Math. Hungar., 2013, 139(3): 228-244

[6] Salimov A. A.. On operators associated with tensor fields. J. Geom., 2010, 99(1–2): 107-145

[7] Yano K., Ako M.. On certain operators associated with tensor fields. Kodai Math. Sem. Rep., 1968, 20: 414-436

[8] Yano K., Ishihara S.. Tangent and cotangent bundles. Pure and Applied Mathematics, 1973, New York: Marcel Dekker, Inc.