We explore relationship between the cut locus of an arbitrary simply connected and compact Riemannian symmetric space and the Cartan polyhedron of corresponding restricted root system, and compute injectivity radius and diameter for every type of irreducible ones.

This research focused on studying the flows of a null Cartan curve specified by velocity and acceleration fields. We have proven that tangential normal velocities are influenced binormal along motion. The fields used to drive time evolution equations for frame torsion curve. objective this work is construct family inextensible curves from initial surface formed obtained numerically visualized. ...

An Abelian gerbe is constructed over classical phase space. The 2–cocycles defining the gerbe are given by Feynman path integrals whose integrands contain the exponential of the Poincaré–Cartan form. The U(1) gauge group on the gerbe has a natural interpretation as the invariance group of the Schroedinger equation on phase space.

Using two dimensional (2D) N = 4 sigma model, with U(1) gauge symmetry, and introducing the ADE Cartan matrices as gauge matrix charges, we build ” toric” hyperKahler eight real dimensional manifolds X8. Dividing by one toric geometry circle action of X8 manifolds, we present examples describing quotients X7 = X8 U(1) of G2 holonomy. In particular, for the Ar Cartan matrix, the quotient space i...

In the field equations of Einstein-Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. This serves as a rough model of space filled with (fermionic) dark matter. From this the Einstein static universe with constant torsion is constructed, generalising the Einstein Cosmos to Einstein-Cartan ...

Using two dimensional (2D) N = 4 sigma model, with U(1) gauge symmetry, and introducing the ADE Cartan matrices as gauge matrix charges, we build ” toric” hyperKahler eight real dimensional manifolds X8. Dividing by one toric geometry circle action of X8 manifolds, we present examples describing quotients X7 = X8 U(1) of G2 holonomy. In particular, for the Ar Cartan matrix, the quotient space i...

Langevin equation describing soft modes in the quark-gluon plasma is reformulated on the loop space. The Cauchy problem for the resulting loop equation is solved for the case when the nonvanishing components of the gauge potential correspond to the Cartan generators of the SU(N)-group and are proportional to a constant unit vector in the Cartan subalgebra. The regularized form of the loop equat...

The so-called ‘soldering’ procedure performed by A.M. Polyakov in [1] for a SL(2,R)gauge theory is geometrically explained in terms of a Cartan connection on second order frames of the projective space RP. The relationship between a Cartan connection and the usual (Ehresmann) connection on a principal bundle allows to gain an appropriate insight into the derivation of the genuine ‘diffeomorphis...