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.

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