The warped product of holomorphic Lie algebroids

Abstract

We introduce the warped product of two holomorphic Finsler algebroids and we define a complex Finsler function on it. We study the Chern-Finsler connections of the bundles and of their product and we investigate their curvatures. We use the geometrical setting of the prolongations of the two bundles to obtain some similar and some different properties from the ones of the warped product of Finsler manifolds.