# A geometric perspective on the method of descent

## 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.

## Key findings

- Derived a new representation formula for tensorial wave equations
- Extended the method of descent to any dimension in a geometric framework
- Applicable to globally hyperbolic Lorentzian spacetimes

## Abstract

We derive a representation formula for the tensorial wave equation $\Box_\bg \phi^I=F^I$ 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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Source: https://tomesphere.com/paper/1703.06458