Construction of the holonomy invariant foliated cocycles on the tangent bundle via formal integrability

Authors : FATEMEH AHANGARI

Pages : 81-102

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :This paper is dedicated to exhaustive structural analysis of the holonomy invariant foliated cocycles on the tangent bundle of an arbitrary $insert ignore into journalissuearticles values(m+n);$-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