A geometric perspective on the method of descent

Qian Wang

arXiv:1703.06458·math.AP·June 13, 2018

A geometric perspective on the method of descent

Qian Wang

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TL;DR

This paper presents a geometric formulation of the method of descent for tensorial wave equations in Lorentzian spacetimes, providing a new representation formula applicable across dimensions.

Contribution

It introduces a geometric perspective on the method of descent, extending its applicability to tensorial wave equations in general dimensions.

Findings

01

Derived a new representation formula for tensorial wave equations

02

Extended the method of descent to any dimension in a geometric framework

03

Applicable to globally hyperbolic Lorentzian spacetimes

Abstract

We derive a representation formula for the tensorial wave equation $□_{\bg} ϕ^{I} = F^{I}$ in globally hyperbolic Lorentzian spacetimes $(\M^{2 + 1}, \bg)$ by giving a geometric formulation of the method of descent which is applicable for any dimension.

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