α-connections in generalized geometry

Special connections in almost paracontact metric geometry

‎Two types of properties for linear connections (natural and almost paracontact metric) are discussed in almost paracontact metric geometry with respect to four linear connections‎: ‎Levi-Civita‎, ‎canonical (Zamkovoy)‎, ‎Golab and generalized dual‎. ‎Their relationship is also analyzed with a special view towards their curvature‎. ‎The particular case of an almost paracosymplectic manifold giv...

Properties of Generalized Berwald Connections

special connections in almost paracontact metric geometry

‎two types of properties for linear connections (natural and almost paracontact metric) are discussed in almost paracontact metric geometry with respect to four linear connections‎: ‎levi-civita‎, ‎canonical (zamkovoy)‎, ‎golab and generalized dual‎. ‎their relationship is also analyzed with a special view towards their curvature‎. ‎the particular case of an almost paracosymplectic manifold giv...

Regular Connections among Generalized Connections

The properties of the space A of regular connections as a subset of the space A of generalized connections in the Ashtekar framework are studied. For every choice of compact structure group and smoothness category for the paths it is determined whether A is dense in A or not. Moreover, it is proven that A has Ashtekar-Lewandowski measure zero for every nontrivial structure group and every smoot...

Connections in sub-Riemannian geometry

We introduce the notion of a connection over a bundle map and apply it to a sub-Riemannian geometry. It is shown that the concepts of normal and abnormal extremals of a sub-Riemannian structure can be characterized as parallel transported sections with respect to these generalized connections. Using this formalism we are able to give necessary and sufficient conditions for the existence of a sp...