Proves κ(F) ≥ √(2n/(n+1)) for almost Hermitian (dim 2n) or quaternion-Hermitian (dim 4n) submanifolds with harmonic fundamental forms, with equality iff the form is parallel and the immersion is a standard Veronese embedding up to totally geodesic inclusion.
Petrunin,Veronese minimizes normal curvatures, arXiv:2408.05909, 2025.↑2
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A lower bound on average normal curvature for closed submanifolds in Riemannian domains is given via an n-trace convexity invariant, extending Petrunin's result to Cartan-Hadamard geodesic balls and similar settings.
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Maximal Normal Curvature and Veronese Rigidity
Proves κ(F) ≥ √(2n/(n+1)) for almost Hermitian (dim 2n) or quaternion-Hermitian (dim 4n) submanifolds with harmonic fundamental forms, with equality iff the form is parallel and the immersion is a standard Veronese embedding up to totally geodesic inclusion.
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Normal curvature bounds for immersions into Riemannian domains
A lower bound on average normal curvature for closed submanifolds in Riemannian domains is given via an n-trace convexity invariant, extending Petrunin's result to Cartan-Hadamard geodesic balls and similar settings.