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arXiv · 0803.2621

Isometric Immersions of Hypersurfaces in 4-dimensional Manifolds via Spinors

Marie-Amélie Lawn·Julien Roth
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Abstract

We give a spinorial characterization of isometrically immersed hypersurfaces into 4-dimensional space forms and product spaces $\M^3(κ)\times\R$, in terms of the existence of particular spinor fields, called generalized Killing spinors or equivalently solutions of a Dirac equation. This generalizes to higher dimensions several recent results for surfaces by T. Friedrich, B. Morel and the two authors. The main argument is the interpretation of the energy-momentum tensor of a generalized Killing spinor as the second fundamental form, possibly up to a tensor depending on the ambient space. As an application, we deduce a non-existence result for hypersurfaces in the 4-dimensional Euclidean space.

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Marie-Amélie Lawn, Julien Roth. 2008-12-09. Isometric Immersions of Hypersurfaces in 4-dimensional Manifolds via Spinors. https://arxiv.org/abs/0803.2621

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