Bi-invariant metric on volume-preserving diffeomorphisms group of a three-dimensional manifold

Autor:	Smolentsev, N. K.
Rok vydání:	2014
Předmět:	Mathematics - Differential Geometry 58D05 58D30 58B20 58J28
Zdroj:	Sib. Math. J. 24 (1983), no. 1, 152 - 159
Druh dokumentu:	Working Paper
Popis:	We show the existence of a weak bi-invariant symmetric nondegenerate 2-form on the volume-preserving diffeomorphism group of a three-dimensional manifold and study its properties. Despite the fact that the space $\mathcal{D}_\mu(M^3)$ is infinite-dimensional, we succeed in defining the signature of the bi-invariant quadric form. It is equal to the $\eta$-invariant of the manifold $M^3$. Comment: 10 pqges
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1401.7415 Zobrazit plný text záznamu View this record from Arxiv