Mapping Among Line Elements
Differential Geometry
2022-09-14 v1 Metric Geometry
Abstract
In this paper, we revisit our paper "Matrix Riccati Equations, Kaluza-Klein, Finsler Spaces, and Mapping Among Manifolds"[1]. We will build mapping among generalized quadratic Hamiltonians and we construct Calabi's Riemmannian Line Elements for non-quadratic and generalized Hamiltonians. As an application, we use conformally flat forms of two general pseudo-Riemannian line elements embedded in two flat manifolds and obtain an analytical and exact solution of the mapping between these two manifolds as well as an infinite set of exact solutions of the associated matrix Riccati equation.
Keywords
Cite
@article{arxiv.2209.05937,
title = {Mapping Among Line Elements},
author = {A. C. V. V. de Siqueira},
journal= {arXiv preprint arXiv:2209.05937},
year = {2022}
}
Comments
24 pages, no figures