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This article is available for purchase or by subscription. See below.
Abstract
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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
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Mathematical Subject Classification
Primary: 53C18, 53C40
Secondary: 58J99
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Milestones
Received: 17 May 2020
Revised: 6 December 2020
Accepted: 14 August 2021
Published: 10 November 2021
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