We show that for the reductive Tannaka groups of semisimple holonomic $\mathscr{D}$-modules on abelian varieties, every Weyl group orbit weights their universal cover is realized by a conic Lagrangian cycle cotangent bundle. Applications include weak solution to Schottky problem in genus five, an obstruction existence summands subvarieties varieties and criterion simplicity arising Lie algebras.

It is shown that the kernels for mean value representations of points in R in terms of the integrals over piecewise smooth hypersurfaces are divergence free vector fields defined by homogeneous functions of degree −(n+1), whose restrictions to the unit sphere are positive and orthogonal to the first harmonics. By Minkowski problem, such a function is the reciprocal of the composition of the Gau...

In this work, we handle timelike Aminov surfaces in E_1^4 with respect to having pointwise one type Gauss map. Firstly, get the laplace of map surface. Then, obtain that there is no surface harmonic and also first kind Minkowski 4-space. Further, yield conditions second kind.

A measurable map T on a measure space induces a representation ΠT of a Cuntz algebra ON when T satisfies a certain condition. For such two maps τ and σ and representations Πτ and Πσ associated with them, we show that Πτ is the restriction of Πσ when τ is a jump transformation of σ. Especially, the Gauss map τ1 and the Farey map σ1 induce representations Πτ1 of O∞ and that Πσ1 of O2, respectivel...

The geometry of minimal surfaces generated by charge 2 Bogomolny monopoles on R is described in terms of the moduli space parameter k. We find that the distribution of Gaussian curvature on the surface reflects the monopole structure. This is elucidated by the behaviour of the Gauss maps of the minimal surfaces. 2000 Mathematics Subject Classification. Primary 53A10; Secondary 53C07, 81T13 §

We study smooth maps t: M -> Ci of a Riemann surface M into the Grassmannian Gi of oriented 2-planes in E2 ' ' and determine necessary and sufficient conditons on t in order that it be the Gauss map of a conformai immersion X: M -» E2 + '. We sometimes view / as an oriented riemannian vector bundle; it is a subbundle of Ej/'. the trivial bundle over M with fibre E2 + l. The necessary and suffic...