Tensor Distributions in the Presence of Degenerate Metrics

TL;DR

This paper develops a framework for tensor distributions and their derivatives on manifolds with degenerate or changing signature metrics, expanding the mathematical tools available for such geometries.

Contribution

It introduces a metric-independent approach to tensor distributions, enabling analysis on manifolds with degenerate or signature-changing metrics.

Findings

Framework for tensor distributions without metric assumptions

Application to manifolds with degenerate metrics

Facilitates analysis of metrics with changing signatures

Abstract

Tensor distributions and their derivatives are described without assuming the presence of a metric. This provides a natural framework for discussing tensor distributions on manifolds with degenerate metrics, including in particular metrics which change signature.