Averaging of isotropic submanifolds

نویسنده

  • Marco Zambon
چکیده

We will give a construction to obtain canonically an “isotropic average“ of given C close isotropic submanifolds of a Kähler manifold. The isotropic average will be C close to the given submanifolds. The construction relies on an averaging procedure by Weinstein and on “Moser’s trick”.

برای دانلود رایگان 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

Isotropic Lagrangian Submanifolds in Complex Space Forms

In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in . We also give a classification of semi-parallel Lagrangian H-umbilical submanifolds.

متن کامل

Submanifold averaging in riemannian and symplectic geometry

We give a construction to obtain canonically an “isotropic average” of given C-close isotropic submanifolds of a symplectic manifold. To do so we use an improvement of Weinstein’s submanifold averaging theorem (obtained in collaboration with H. Karcher) and apply “Moser’s trick”. We also present an application to Hamiltonian group actions.

متن کامل

Contact Geometry

2 Contact manifolds 4 2.1 Contact manifolds and their submanifolds . . . . . . . . . . . . . . 6 2.2 Gray stability and the Moser trick . . . . . . . . . . . . . . . . . . 13 2.3 Contact Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Darboux’s theorem and neighbourhood theorems . . . . . . . . . . 17 2.4.1 Darboux’s theorem . . . . . . . . . . . . . . . . . . . . . . . 17...

متن کامل

Diffeomorphisms Preserving Symplectic Data on Submanifolds

We characterize general symplectic manifolds and their structure groups through a family of isotropic or symplectic submanifolds and their diffeomorphic invariance. In this way we obtain a complete geometric characterization of symplectic diffeomorphisms and a reinterpretation of symplectomorphisms as diffeomorphisms acting purely on isotropic or symplectic submanifolds. DOI: 10.1134/S008154380...

متن کامل

Volume Minimization and Estimates for Certain Isotropic Submanifolds in Complex Projective Spaces

In this note we show the following result using the integral-geometric formula of R. Howard: Consider the totally geodesic RP 2m in CP n. When it minimizes volume among the isotropic submanifolds in the same Z/2 homology class in CP n (but not among all submanifolds in this Z/2 homology class). Also the totally geodesic RP 2m−1 minimizes volume in its Hamiltonian deformation class in CP n. As a...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008