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Quantifier elimination for elementary geometry and elementary affine geometry
(Wiley VCH Verlag, 2012-11)
We introduce new first-order languages for the elementary n-dimensional geometry and elementary n-dimensional affine geometry (n ≥ 2), based on extending FO(β≡) and FO(β), respectively, with new function symbols. Here, β ...
The Geometry of Locally Symmetric Affine Surfaces
(Springer, 2018-03)
We examine the local geometry of affine surfaces which are locally symmetric. There are six non-isomorphic local geometries. We realize these examples as type A, type B, and type C geometries using a result of Opozda and ...
Affine skeletons and monge-ampere equations
(Siam Publications, 2009)
An important question about a. ne skeletons is the existence of differential equations that are related to the 'affine distance' and the 'area distance' (hence to a. ne skeletons) in the same way the Eikonal equation is ...
Dynamo effects and geometrical origin of the alpha term in affine theory of gravity
(Maik Nauka Publishing / Springer SBM, 2017-12)
Dynamo effect is considered in the context of an Unified field theoretical model based in affine geometries. We show that there exists an analog “α-term” in the equations that has a purely geometric origin, in sharp contrast ...
A fast marching method for the area based affine distance
(Springer, 2008-01)
In a previous paper, it was proved that the area based affine distance of a convex region in the plane satisfies a non-homogeneous Monge-Ampere differential equation. Based on this equation, in this paper we propose a fast ...
Cones and Cartan geometry
(Elsevier Science, 2021-10)
We show that the extended principal bundle of a Cartan geometry of type (A(m,R),GL(m,R)), endowed with its extended connection ωˆ, is isomorphic to the principal A(m,R)-bundle of affine frames endowed with the affine ...
Affine properties of convex equal-area polygons
(Springer, 2012-10)
In this paper we discuss some affine properties of convex equal-area polygons, which are convex polygons such that all triangles formed by three consecutive vertices have the same area. Besides being able to approximate ...
Envelope of Mid-Planes of a surface and some classical notions of affine differential geometry
(Results in Mathematics, 2018)
Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)
(ELSEVIER SCIENCE BV, 2009)
In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an ...