On real and complex Berwald connections associated to strongly convex weakly Kähler–Finsler metric

Properties of Generalized Berwald Connections

Properties of Generalized Berwald Connections

Recently the present authors introduced a general class of Finsler connections which leads to a smart representation of connection theory in Finsler geometry and yields to a classification of Finsler connections into the three classes. Here the properties of one of these classes namely the Berwald-type connections which contains Berwald and Chern(Rund) connections as a special case is studied. ...

The Berwald-type linearisation of generalised connections

We study the existence of a natural ‘linearisation’ process for generalised connections on an affine bundle. It is shown that this leads to an affine generalised connection over a prolonged bundle, which is the analogue of what is called a connection of Berwald type in the standard theory of connections. Various new insights are being obtained in the fine structure of affine bundles over an anc...

properties of generalized berwald connections

Hexagonal 2-complexes Have a Strongly Convex Metric

We give two distinct proofs for the fact that any finite simply connected hexagonal 2-complex has a strongly convex metric. In our first proof we show that these complexes are CAT(0) spaces, while the second proof makes use of the fact that finite, simply connected hexagonal 2-complexes are collapsible. Both proofs rely on the fact that hexagonal 2-complexes have the 12-property.