Higher Willmore Energies from tractor coupled GJMS operators

2024/11/04 by Allen, Ben F., Gover, Rod
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.01835

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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