Laplace operators on holomorphic Lie algebroids

Abstract

The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator for forms defined on the prolongation of the algebroid. All the Laplace operators considered in the paper are also locally expressed using the Chern-Finsler connection of the algebroid.

Keywords

• holomorphic lie algebroid
• anchor map
• laplacian for functions
• laplacian for forms
• nonlinear connection
• prolongation
• primary 17b66
• 53b40
• secondary 53b35
• 53b21