Geometry of product complex Cartan manifolds

Abstract

In this paper we consider the product of two complex Cartan manifolds, the outcome being a class of product complex Cartan spaces. Then, we study the relationships between the geometric objects of a product complex Cartan space and its components, (e.g. Chern-Cartan complex nonlinear connection, Cartan tensors). By means of these, we establish the necessary and sufficient conditions under which a product complex Cartan space is Landsberg-Cartan or Berwald-Cartan or it has some other properties.

Keywords

• complex cartan metric
• product manifold
• landsberg- and berwald-cartan metrics
• primary 53c60
• secondary 53b40