We introduce a notion of a non-Abelian loop gauge field defined on points in loop space. For this purpose we first find an infinite-dimensional tensor product representation of the Lie algebra which is particularly suited for fields on loop space. We define the non-Abelian Wilson surface as a ‘time’ ordered exponential in terms of this loop gauge field and show that it is reparametrization inva...

in this paper we introduce the concept of generalized baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. we give some inequalities for the generalized baer-invariant of a pair of finite groups, when ? is considered to be the schur-baer variety. further, we present a sufficient condition under which the order of the generalized baer-invariant of a pair of finite ...

Many image-rotation invariant texture classification approaches have been presented previously. This paper proposes a novel scheme that is surface-rotation invariant. It uses the eigenvalues of a surface’s gradient-space distribution as its features. Unlike the partial derivatives, from which they are computed, these eigenvalue features are invariant to surface rotation. First we show that a si...

In this short review we look at recent advances in Schramm-Loewner Evolution (SLE) theory and its application to critical phenomena. The application of SLE goes beyond critical systems to other time dependent, scale invariant phenomena such as turbulence, sand-piles and watersheds. Through the use of SLE, the evolution of conformally invariant paths on the complex plane can be followed; hence a...

This paper presents a novel approach to represent spatiotemporal visual information. We introduce a surface-based shape model whose structure is invariant to surface variations over time to describe 3D dynamic surfaces (e.g., obtained from multiview video capture). The descriptor is defined as a graph lying on object surfaces and anchored to invariant local features (e.g., extremal points). Geo...

A surface in homogenous space Sol is said to be an invariant surface if it is invariant under some of the two 1-parameter groups of isometries of the ambient space whose fix point sets are totally geodesic surfaces. In this work we study invariant surfaces that satisfy a certain condition on their curvatures. We classify invariant surfaces with constant mean curvature and constant Gaussian curv...