PARALLELISM OF DISTRIBUTIONS AND GEODESICS ON F(±a2; ±b2)-STRUCTURE LAGRANGIAN MANIFOLD

Mohammad Nazrul Islam Khan, Lovejoy S. Das

DOI Number
https://doi.org/10.22190/FUMI200420013K
First page
157
Last page
163

Abstract


This paper deals with the Lagrange vertical structure on the vertical space TV (E) endowed with a non null (1,1) tensor field FV satisfying (Fv2-a2)(Fv2+a2)(Fv2 - b2)(Fv2 + b2) = 0. In this paper, the authors have proved that if an almost product structure P on the tangent space of a 2n-dimensional Lagrange manifold E is defined and the F(±a2; ±b2)-structure on the vertical tangent space TV (E) is given, then it is possible to define the similar structure on the horizontal subspace TH(E) and also on T(E). In the next section, we have proved some theorems and have obtained conditions under which the distribution L and M are r-parallel, r¯ anti half parallel when r = r¯ . The last section is devoted to proving theorems on geodesics on the Lagrange manifold


Keywords

Distribution, Parallelism, Geodesic, Almost product structure.

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References


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DOI: https://doi.org/10.22190/FUMI200420013K

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