2022/03/18 by Mahouton Norbert Hounkonnou, Hounkonnou, Mahouton Norbert, Mahougnon Justin Landalidji +3
Mathematics · Medicine · Physics and Astronomy · #37C10 #37J35 #37K05 #37K10 #Advanced Differential Geometry Research #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Ophthalmology and Eye Disorders
paper · pdf · doi:10.48550/arxiv.2203.10096
openalex publication_date 2022/03/18 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
We show that a Minkowski phase space endowed with a bracket relatively to a conformable differential realizes a Poisson algebra, confering a bi-Hamiltonian structure to the resulting manifold. We infer that the related Hamiltonian vector field is an infinitesimal Noether symmetry, and compute the corresponding deformed recursion operator. Besides, using the Hamiltonian-Jacobi separability, we construct recursion operators for Hamiltonian vector fields in conformable Poisson-Schwarzschild and Friedmann-Lemaître-Robertson-Walker (FLRW) manifolds, and derive related constants of motion, Christoffel symbols, components of Riemann and Ricci tensors, Ricci constant and components of Einstein tensor. We highlight the existence of a hierarchy of bi-Hamiltonian structures in both the manifolds, and compute a family of recursion operators and master symmetries generating the constants of motion.