Closed three-manifolds as hypersurfaces of Euclidean four-space: compactness, the homogeneous geometries, and total absolute curvature

Abstract

Let \((\Sigma, g)\) be a closed Riemannian three-manifold, and let \(\mathbb M = -G\) be its negative Einstein endomorphism. Where \(\det\mathbb M > 0\), the companion paper {[}MA{]} reduces realizability as a hypersurface of \(E^4\) to one equation, \(F(g) = 0\), and studies it locally. Here we treat the global questions.

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