Laplacian and codifferential operators on p-forms in (Anti)-de Sitter spaces: restriction and continuation

TL;DR

This paper derives explicit formulas for restricting and continuing differential operators on p-forms between (Anti)-de Sitter spaces and Minkowski space, aiding in understanding geometric and physical properties across these spaces.

Contribution

It provides the first explicit restriction and continuation formulas for codifferential and Laplace-de Rham operators on p-forms between (Anti)-de Sitter and Minkowski spaces.

Findings

Explicit restriction formulas for operators on p-forms.

Explicit continuation formulas for operators on p-forms.

Enhanced understanding of geometric relations between spaces.

Abstract

We derive explicit restriction and continuation formulas between n-dimensional (Anti)-de Sitter spaces and the (n + 1)-dimensional Minkowskian ambient space for the codifferential and Laplace-de Rham operators acting on p-forms.