Unknottedness of real Lagrangian tori in $$S^2\times S^2$$
نویسندگان
چکیده
منابع مشابه
Lagrangian unknottedness in Stein surfaces
We show that the space of Lagrangian spheres inside the cotangent bundle of the 2-sphere is contractible. We then discuss the phenomenon of Lagrangian unknottedness in other Stein surfaces. There exist homotopic Lagrangian spheres which are not Hamiltonian isotopic, but we show that in a typical case all such spheres are still equivalent under a symplectomorphism.
متن کاملMinimal Lagrangian tori in Kahler-Einstein manifolds
In this paper we use structure preserving torus actions on KahlerEinstein manifolds to construct minimal Lagrangian submanifolds. Our main result is: Let N be a Kahler-Einstein manifold with positive scalar curvature with an effective T -action. Then precisely one regular orbit L of the T -action is a minimal Lagrangian submanifold of N . Moreover there is an (n− 1)-torus T n−1 ⊂ T n and a sequ...
متن کاملBScan - lagrangian tori in projective spaces
Here we discuss the following situation. Consider CP with the standard symplectic form ω such that its cohomology class [ω] ∈ H(CP) is a generator of H(CP). It’s very well known, see f.e. [3], that the canonical class K of the projective space equals to −(n+1)[ω]. Consider the anticanonical line bundle K∗ → CP and fix a connection a on it such that the curvature form Fa is proportional to the s...
متن کاملNon-isotopic Lagrangian Tori in Elliptic Surfaces
We construct the first example of an infinite family of homotopic but pairwise smoothly non-isotopic Lagrangian tori in the rational elliptic surface E(1) = P2#9P2. Furthermore, we show that any two of these tori are smoothly equivalent, i.e., there exists an orientation-preserving selfdiffeomorphism of E(1) that carries one torus to the other. Our construction can be generalized for many other...
متن کاملSome Examples of Special Lagrangian Tori
The purpose of this note is to point out some very elementary examples of special Lagrangian tori in certain Calabi-Yau manifolds that occur as hypersurfaces in complex projective space. All of these are constructed as real slices of smooth hypersurfaces defined over the reals. This method of constructing special Lagrangian submanifolds is, of course, well known. What does not appear to be in t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2020
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-020-02049-7