J-holomorphic curves and Dirac-harmonic maps
نویسندگان
چکیده
منابع مشابه
Regularity of Dirac-harmonic maps
For any n-dimensional compact spin Riemannian manifold M with a given spin structure and a spinor bundle ΣM , and any compact Riemannian manifold N , we show an ǫ-regularity theorem for weakly Dirac-harmonic maps (φ, ψ) : M ⊗ΣM → N ⊗ φ∗TN . As a consequence, any weakly Dirac-harmonic map is proven to be smooth when n = 2. A weak convergence theorem for approximate Dirac-harmonic maps is establi...
متن کاملLecture 6: J-holomorphic Curves and Applications
Let (M,ω) be a symplectic manifold of dimension 2n, and let J ∈ J (M,ω) be an ω-compatible almost complex structure. Let gJ(·, ·) ≡ ω(·, J ·) be the corresponding hermitian metric (i.e. J-invariant Riemannian metric) on M . Let (Σ, j) be a Riemann surface (not necessarily compact) with complex structure j. A smooth map u : Σ → M is called a (J, j)-holomorphic map (or simply a J-holomorphic map)...
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We study the J−holomorphic curves in the symplectization of the contact manifolds and prove that there exists at least one periodic Reeb orbits in any closed contact manifold with any contact form by using the well-known Gromov's nonlinear Fredholm alternative for J−holomorphic curves. As a corollary, we give a complete solution on the well-known Weinstein conjecture.
متن کاملJ -holomorphic curves, moment maps, and invariants of Hamiltonian group actions
3 Invariants of Hamiltonian group actions 17 3.1 An action functional . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Symplectic reduction . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Hamiltonian perturbations . . . . . . . . . . . . . . . . . . . . 24 3.4 Moduli spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.5 Fredholm theory . . . . . . . . . . . . . . . . . . ...
متن کاملSe p 19 99 J - holomorphic curves , moment maps , and invariants of Hamiltonian group actions
3 Invariants of Hamiltonian group actions 17 3.1 An action functional . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Symplectic reduction . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Hamiltonian perturbations . . . . . . . . . . . . . . . . . . . . 24 3.4 Moduli spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.5 Fredholm theory . . . . . . . . . . . . . . . . . . ...
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2020
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2019.101587