Higher Willmore Energies from tractor coupled GJMS operators

Ben F. Allen; Rod Gover

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arXiv · 2411.01835

Higher Willmore Energies from tractor coupled GJMS operators

Ben F. Allen·Rod Gover

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Abstract

We define and construct a conformally invariant energy for closed smoothly immersed submanifolds of even dimension, but of arbitrary codimension, in conformally flat Riemannian manifolds. This is a higher dimensional analogue of the Willmore energy for immersed surfaces and is given directly via a coupling of the tractor connection to the (submanifold critical) GJMS operators. In the case where the submanifold is of dimension 4 we compare this to other energies, including one found using a second simple construction that uses $Q$-operators.

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BibTeX RIS

Ben F. Allen, Rod Gover. 2024-11-04. Higher Willmore Energies from tractor coupled GJMS operators. https://arxiv.org/abs/2411.01835

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