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

Autor:	Lovejoy S. Das, Mohammad Nazrul Islam Khan
Rok vydání:	2021
Předmět:	Physics Section (fiber bundle) Pure mathematics Geodesic Vertical tangent Tangent space Space (mathematics) Distribution (differential geometry) Manifold Tensor field
Zdroj:	Facta Universitatis, Series: Mathematics and Informatics. :157
ISSN:	2406-047X 0352-9665
Popis:	This paper deals with the Lagrange vertical structure on the vertical space T V ( E ) endowed with a non null (1,1) tensor field F V satisfying ( F v 2 - a 2 )( F v 2 + a 2 )( F v 2 - b 2 )( F v 2 + b 2 ) = 0. In this paper, the authors have proved that if an almost product structure P on the tangent space of a 2 n -dimensional Lagrange manifold E is defined and the F ( ± a 2 ; ± b 2 )-structure on the vertical tangent space T V ( E ) is given, then it is possible to define the similar structure on the horizontal subspace T H ( 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
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::491cce3d813031e75ab3b61f1ee5b9d7 https://doi.org/10.22190/fumi200420013k Zobrazit plný text záznamu