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The Geometry of Extremal Elements in a Lie Algebra
Let L be a simple finite-dimensional Lie algebra over an algebraically closed field of characteristic distinct from 2 and from 3. Then L contains an...
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Curvature line parametrized surfaces and orthogonal coordinate systems: discretization with Dupin cyclides
Cyclidic nets are introduced as discrete analogs of curvature line parametrized surfaces and orthogonal coordinate systems. A 2-dimensional cyclidic...
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The Apollonius contact problem and Lie contact geometry
A simple classification of triples of Lie cycles is given. The class of each triad determines the number of solutions to the associated oriented...
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Duality for Curves in Affine Plane Geometry
The dual of a plane curve in equiaffine geometry is defined as a curve in the space of conics. The image and inverse of this duality are described....
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On the Fundamental Theorems of the Geometries of Symmetric Matrices
In the present paper the relation between the fundamental theorem of S n (F) and the fundamental theorem of P S n (F)is studied geometrically.
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A Characterization of Twin Buildings by Twin Apartments
A twin building is a pair of buildings along with a certain ’codistance' between chambers of one building, and chambers of the other. All spherical...
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On the geometry of hyperbolic cycles
A hyperbolic cycle is a point or an oriented hypersphere of an n -dimensional hyperbolic space. We determine all surjective map**s from the set of...
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