Time-dependent Lagrangian energy systems on supermanifolds with graph bundles
type: Item
instance of: scholarly article
title: Time-dependent Lagrangian energy systems on supermanifolds with graph bundles
zbMATH Open document ID: 1477.58003
DOI: 10.1155/2021/5528123
author: Cansel Aycan
author: Simge Simsek
published in: Journal of Mathematics
publication date: 2021-06-28T00:00:00Z
review text: Summary: The aim of this article is firstly to improve time-dependent Lagrangian energy equations using the super jet bundles on supermanifolds. Later, we adapted this study to the graph bundle. Thus, we created a graph bundle by examining the graph manifold structure in superspace. The geometric structures obtained for the mechanical energy system with superbundle coordinates were reexamined with the graph bundle coordinates. Thus, we were able to calculate the energy that occurs during the motion of a particle when we examine this motion with graph points. The supercoordinates on the superbundle structure of supermanifolds have been given for body and soul and also even and odd dimensions. We have given the geometric interpretation of this property in coordinates for the movement on graph points. Lagrangian energy equations have been applied to the presented example, and the advantage of examining the movement with graph points was presented. In this article, we will use the graph theory to determine the optimal motion, velocity, and energy of the particle, due to graph points. This study showed a physical application and interpretation of supervelocity and supertime dimensions in super-Lagrangian energy equations utilizing graph theory.
Mathematics Subject Classification ID: 58A20
Mathematics Subject Classification ID: 58A50
zbMATH DE Number: 7363792
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5528123
OpenAlex ID: W3157796884
cites work: Topological and geometric properties of graph-manifolds
cites work: Gruppen mit Zentrum und 3-dimensionale Mannigfaltigkeiten
cites work: Recognizing Cartesian graph bundles
cites work: Improving Lagrangian energy equations on Kähler jet bundles
cites work: Singular Lagrangian Systems on Jet Bundles
cites work: Lagrangian submanifolds and the Euler-Lagrange equations in higher-order mechanics
cites work: Q3361582
cites work: Classical and quantum mechanics with time-dependent parameters
cites work: Superspaces and supersymmetries
cites work: Erratum: Cohomology of the structure sheaf of real and complex supermanifolds [J. Math. Phys. 2 9, 1789 (1988)]
cites work: On curves and jets of curves on supermanifolds
cites work: Vector representations of graphs
cites work: Q4871313
cites work: SUPERMETRICS ON SUPERMANIFOLDS
description: scientific article; zbMATH DE number 7363792