Chern–Simons forms for ℝ-linear connections on Lie algebroids

This paper considers the Chern–Simons forms for [Formula: see text]-linear connections on Lie algebroids. A generalized Chern–Simons formula for such [Formula: see text]-linear connections is obtained. We apply it to define the Chern character and secondary characteristic classes for [Formula: see text]-linear connections of Lie algebroids.

The Secondary Characteristic Classes

Changing the representation bundle from T to T ⊗ T∗ gives a sequence where both torsion and curvature live. Vanishing of the curvature gives rise to some closed forms.