The symplectic Hadamard question
arXiv:2607.12940
summary
The paper proves that any simply connected symplectic manifold that admits a complete compatible metric with nonpositive curvature is symplectomorphic to Euclidean space ℝ^{2n} with its standard symplectic form, resolving the symplectic Hadamard question of McDuff‑Salamon.
Abstract
We show that a simply connected symplectic manifold admitting a complete nonpositively curved compatible metric is symplectomorphic to R^{2n} with its standard symplectic form. This answers the "symplectic Hadamard question" of McDuff-Salamon in the affirmative.
some Math/AI aspects around this work are discussed in section 1.1
Topics & keywords
#symplectic manifolds#nonpositive curvature#Hadamard question#symplectomorphism#R^{2n}#compatible metricssimply connectedcomplete metricnonpositive curvaturesymplectomorphicstandard symplectic formMcDuff‑Salamon