Metallic structure on Lagrangian manifold

Geeta Verma

doi:10.56424/jts.v14i01.10610

Geeta Verma Department of Mathematics Shri Ramswaroop memorial group of professional colleges, Lucknow, India.

DOI: https://doi.org/10.56424/jts.v14i01.10610

Keywords: Metallic structure; Lagrangian manifold; vertical space.

Abstract

In this paper, the author convention with the Lagrange vertical structure on the vertical space TV (E) endowed with a non null (1,1) tensor field FV satisfying metallic structure F2 − αF − βI = 0. The horizontal subspace TH(E) is applied on the same structure. Next, some theorems are proved and obtained conditions under which the distribution L and M are ∇-parallel, ¯∇ anti half parallel when ∇ = ¯∇. Lastly, certain theorems on geodesics on the Lagrange manifold are deduced.