ASYMPTOTIC LINKING INVARIANTS FOR RKACTIONS IN COMPACT RIEMANNIAN MANIFOLDS / ÍNDICES DE ENLAÇAMENTO ASSINTÓTICO PARA AÇÕES DE RK EM VARIEDADES RIEMANNIANAS COMPACTAS

AUTOR(ES)
DATA DE PUBLICAÇÃO

2005

RESUMO

V.I. Arnold, in his paper The algebraic Hopf invariant and its applications published in 1986, considered a compact domain (ômega maiúsculo) in R3 with a smooth boundary and trivial homology and two divergence free vector fields X and Y in (ômega maiúsculo) tangent to the boundary. He defined an asymptotic linking invariant lk(X; Y ) and a Hopf invariant associated to X and Y by the integral I(X; Y ) = (integral em ômega maiúsculo de alfa produto d-beta) where (d-alfa) = iX-vol e (d-beta) = iy- vol. He showed that que I(X; Y ) = lk(X; Y ). In the present work we extend these definitions of the asymptotic linking invariant lk(fi maiúsculo,xi maiúsculo) and the Hopf invariant I(fi maiúsculo,xi maiúsculo) where (fi maiúsculo) and (xi maiúsculo) are actions Rk and Rs, k+s = n-1 by volume preserving diffeomorphisms, on the closed unit ball (ômega maiúsculo n) in and we show lk (fi maiúsculo, xi maiúsculo) = I(fi maiúsculo,xi maiúsculo).

ASSUNTO(S)

indice de enlacamento assintotico algebra exterior law of biot-savart vector field acoes de rk lei de biot-savart rk-action exterior algebra campos vetoriais asymptotic linking invariant

ACESSO AO ARTIGO

Documentos Relacionados