- Turkish Journal of Mathematics
- Vol: 43 Issue: 1
- Construction of the holonomy invariant foliated cocycles on the tangent bundle via formal integrabil...
Construction of the holonomy invariant foliated cocycles on the tangent bundle via formal integrability
Authors : Fatemeh Ahangari
Pages : 81-102
View : 8 | Download : 7
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :This paper is dedicated to exhaustive structural analysis of the holonomy invariant foliated cocycles on the tangent bundle of an arbitrary $(m+n)$-dimensional manifold. For this purpose, by applying Spencer theory of formal integrability, sufficient conditions for the metric associated with the semispray $S$ are determined to extend to a transverse metric for the lifted foliated cocycle on $TM$. Accordingly, this geometric structure converts to a holonomy invariant foliated cocycle on the tangent space, which is totally adapted to the Helmholtz conditions.Keywords : Foliated cocycle, holonomy group, metrizability, formal integrability, transverse metric