Iterated differential forms: Riemannian geometry revisited

Differential Geometry of Gerbes and Differential Forms

We discuss certain aspects of the combinatorial approach to the differential geometry of non-abelian gerbes due to W. Messing and the author [5], and give a more direct derivation of the associated cocycle equations. This leads us to a more restrictive definition than in [5] of the corresponding coboundary relations. We also show that the diagrammatic proofs of certain local curving and curvatu...

A Geometry Preserving Kernel over Riemannian Manifolds

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

Riemannian geometry

Differential Forms and Odd Symplectic Geometry

We remind the main facts about the odd Laplacian acting on half-densities on an odd symplectic manifold and discuss a homological interpretation for it suggested recently by P. Ševera. We study relations of odd symplectic geometry with classical objects. We show that the Berezinian of a canonical transformation for an odd symplectic form is a polynomial in matrix entries and a complete square. ...

Ma Thema Tics : a . D . Michal " Riemannian " Differential Geometry In