2025/11/14 by Yamamoto, Hikaru
#53C21 #53C40 #53C42 #53D12 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2511.10973
For an immersed Lagrangian submanifold L in a Kähler manifold (M,ω), there exists a symplectic local diffeomorphism from a tubular neighborhood of the image of the zero section in the normal bundle T\botL of L, equipped with a canonical symplectic form ω, to (M,ω) whose restriction to L is the identity map by Weinstein's Lagrangian tubular neighborhood theorem, where the image of the zero section in T\botL is identified with L. In this paper, we give a lower bound for the supremum of the radii of tubular neighborhoods that have such a symplectic diffeomorphism into (M,ω) from below by a constant explicitly given in terms of up to second derivatives of the Riemannian curvature tensor of M and the second fundamental form of L. We also give a similar lower bound in the case where L is compact and embedded.