Non-existence of higher-order conformal fundamental forms in odd dimensions

2025/09/24 by Blitz, Samuel
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.20554

Abstract

Conformal fundamental forms populate a minimal generating set for low differential order invariants of conformal hypersurface embeddings. In this work we complete the characterization of conformal fundamental forms by proving the general non-existence of higher-order conformal fundamental forms when the embedded hypersurface is even dimensional.

Citations

• A Gauss-Bonnet formula for the renormalized area of minimal submanifolds of Poincaré-Einstein manifolds
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• A Sharp Characterization of the Willmore Invariant
• Conformal Fundamental Forms and the Asymptotically Poincaré--Einstein Condition
• Volume renormalization for singular Yamabe metrics
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• An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity
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Related

• Toward a Classification of Conformal Hypersurface Invariants
• Conformal hypersurface invariants and Bach-type Boundary Problems
• Conformal Fundamental Forms and the Asymptotically Poincaré--Einstein Condition
• Non-linear partial differential equations in conformal geometry
• Conformal hypersurface geometry via a boundary Loewner-Nirenberg-Yamabe\n problem