Vol. 314, No. 2, 2021

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

Stephen E. McKeown

Vol. 314 (2021), No. 2, 411–424
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.

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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
Authors
Stephen E. McKeown
University of Texas at Dallas
Richardson, TX
United States