Symplectic Critical Surfaces in Kähler Surfaces

نویسندگان

  • XIAOLI HAN
  • JIAYU LI
چکیده

Let M be a Kähler surface and Σ be a closed symplectic surface which is smoothly immersed in M . Let α be the Kähler angle of Σ in M . We first deduce the Euler-Lagrange equation of the functional L = ∫ Σ 1 cosα dμ in the class of symplectic surfaces. It is cos αH = (J(J∇ cosα)), where H is the mean curvature vector of Σ in M , J is the complex structure compatible with the Kähler form ω in M , which is an elliptic equation. We then study the properties of the equation.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Family Gromov-Witten Invariants for Kähler Surfaces

We use analytic methods to define Family Gromov-Witten Invariants for Kähler surfaces. We prove that these are well-defined invariants of the deformation class of the Kähler structure. Gromov-Witten invariants are counts of holomorphic curves in a symplectic manifold X. To define them using the analytic approach one chooses an almost complex structure J compatible with the symplectic structure ...

متن کامل

Critical Symplectic Connections on Surfaces

The space of symplectic connections on a symplectic manifold is a symplectic affine space. M. Cahen and S. Gutt showed that the action of the group of Hamiltonian diffeomorphisms on this space is Hamiltonian and calculated the moment map. This is analogous to, but distinct from, the action of Hamiltonian diffeomorphisms on the space of compatible almost complex structures that motivates study o...

متن کامل

On a Theorem of Peters on Automorphisms of Kähler Surfaces

For any Kähler surface which admits no nonzero holomorphic vectorfields, we consider the group of holomorphic automorphisms which induce identity on the second rational cohomology. Assuming the canonical linear system is without base points and fixed components, C.A.M. Peters [12] showed that this group is trivial except when the Kähler surface is of general type and either c1 = 2c2 or c 2 1 = ...

متن کامل

An obstruction bundle relating Gromov-Witten invariants of curves and Kähler surfaces

In [LP] the authors defined symplectic “Local Gromov-Witten invariants” associated to spin curves and showed that the GW invariants of a Kähler surface X with pg > 0 are a sum of such local GW invariants. This paper describes how the local GW invariants arise from an obstruction bundle (in the sense of Taubes [T]) over the space of stable maps into curves. Together with the results of [LP], thi...

متن کامل

Ruled 4-manifolds and isotopies of symplectic surfaces

We study symplectic surfaces in ruled symplectic 4-manifolds which are disjoint from a given symplectic section. As a consequence, in any symplectic 4-manifold two symplectic surfaces which are C close must be Hamiltonian isotopic.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008