On deformed Riemannian extensions associated with twin Norden metrics

Abstract

The main purpose of this paper is to study the deformed Riemannian extension ^∇ g+ ^V G ^•• in the cotangent bundle, where G is a twin Norden metric on the base manifold.

Keywords

Riemannian extension / Cotangent bundle / Vertical and complete lifts / Horizontal lifts / Deformed metric / Twin Norden metric

References

[1] Aras M. The metric connection with respect to the synectic metric. Hacet. J. Math. Stat., 2012, 41(2): 169-173

[2] Aslanci S, Kazimova S, Salimov A A. Some notes concerning Riemannian extensions. Ukrainian Math. J., 2010, 62(5): 661-675

[3] Bonome A, Castro R, Hervella L M, Matsushita Y. Construction of Norden structures on neutral 4-manifolds. JP J. Geom. Topol., 2005, 5(2): 121-140

[4] Salimov A. Tensor Operators and Their Applications, 2012, New York: Nova Science Publishers

[5] Talantova N V, Shirokov A P. A remark on a certain metric in the tangent bundle. Izv. Vys. Ucebn. Zaved. Matematika, 1975, 157(6): 143-146

[6] Vishnevskii V V, Shirokov A P, Shurygin V V. Spaces over Algebras, 1985, Kazan: Kazanskii Gosudarstvennyi Universitet

[7] Yano K, Ishihara S. Tangent and Cotangent Bundles, 1973, New York: Mercel Dekker, Inc.