Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1705-19
Keywords
Foliated cocycle, holonomy group, metrizability, formal integrability, transverse metric
First Page
81
Last Page
102
Recommended Citation
AHANGARI, F (2019). Construction of the holonomy invariantfoliated cocycles on the tangent bundle via formal integrability. Turkish Journal of Mathematics 43 (1): 81-102. https://doi.org/10.3906/mat-1705-19
