Mapping among manifolds 1

TL;DR

This paper develops a modified Hamiltonian formalism to map geometric objects like Jacobi fields and metric tensors among manifolds, demonstrating its application by mapping a general Riemannian manifold to a maximally symmetric spacetime.

Contribution

It introduces a novel modified Hamiltonian approach for mapping geometric objects between manifolds, extending the tools for geometric analysis.

Findings

Successfully mapped Jacobi fields and metric tensors among manifolds.

Mapped a general n-dimensional Riemannian manifold to a maximally symmetric spacetime.

Established a new formalism for geometric object transformations.

Abstract

In this paper we have build the modified Hamiltonian formalism for geometric objects like the Jacobi fields and metric tensors. In this approach Jacobi fields and metric tensors are mapped among manifold. As an application, we have mapped a general n-dimensional Riemannian manifold to a n-dimensional maximally symmetric spacetime.