Double groupoids and crossed modules
Double Points on Characteristics. A fixed surface of a moving space will envelope a surface of the fixed space , if we move with respect to . In the general case at each moment of the one-parameter motion there exists a curve on , along which the position of and the enveloped surface are in contact. In the paper we study the interesting special case, where has some double point . This depends on relations between differential geometric properties in the neighbourhood of of the...
The notions of the dual double vector bundle and the dual double vector bundle morphism are defined. Theorems on canonical isomorphisms are formulated and proved. Several examples are given.
The Clifford tori in constitute a one-parameter family of flat, two-dimensional, constant mean curvature (CMC) submanifolds. This paper demonstrates that new, topologically non-trivial CMC surfaces resembling a pair of neighbouring Clifford tori connected at a sub-lattice consisting of at least two points by small catenoidal bridges can be constructed by perturbative PDE methods. That is, one can create a submanifold that has almost everywhere constant mean curvature by gluing a re-scaled catenoid...
We consider doubly warped product (DWP) Finsler manifolds with some non-Riemannian curvature properties. First, we study Berwald and isotropic mean Berwald DWP-Finsler manifolds. Then we prove that every proper Douglas DWP-Finsler manifold is Riemannian. We show that a proper DWP-manifold is Landsbergian if and only if it is Berwaldian. Then we prove that every relatively isotropic Landsberg DWP-manifold is a Landsberg manifold. We show that a relatively isotropic mean Landsberg warped product manifold...
We establish sharp inequalities for C-totally real doubly warped product submanifolds in (κ,μ)-contact space forms and in non-Sasakian (κ,μ)-contact metric manifolds.
One gives the links between the notions of singular foliations, Γ-structures and momentum mapping in the context of symplectic geometry.