Extrinsic curvature and conformal Gauss–Bonnet for four-manifolds with corner

Stephen E. McKeown

Vol. 314 (2021), No. 2, 411–424

DOI: 10.2140/pjm.2021.314.411

Abstract

This paper defines two new extrinsic curvature quantities on the corner of a four-dimensional Riemannian manifold with corner. One of these is a pointwise conformal invariant, and the conformal transformation of the other is governed by a new linear second-order pointwise conformally invariant partial differential operator. The Gauss–Bonnet theorem is then stated in terms of these quantities.

Keywords

Gauss–Bonnet with corners, conformal geometry, corners, corner operators, manifolds with edges

Mathematical Subject Classification

Primary: 53C18, 53C40

Secondary: 58J99

Milestones

Received: 17 May 2020

Revised: 6 December 2020

Accepted: 14 August 2021

Published: 10 November 2021