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.
Title resolution pending
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.DG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
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.
citing papers explorer
-
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.
-
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.