Metric characterizations of spherical and Euclidean buildings

Characterizations of Slant Ruled Surfaces in the Euclidean 3-space

In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...

Euclidean and circum-Euclidean distance matrices: Characterizations and linear preservers

Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.

Combing Euclidean buildings

For an arbitrary Euclidean building we define a certain combing, which satisfies the “fellow traveller property” and admits a recursive definition. Using this combing we prove that any group acting freely, cocompactly and by order preserving automorphisms on a Euclidean building of one of the types An, Bn, Cn admits a biautomatic structure. AMS Classification numbers Primary: 20F32

Metric and Euclidean TSP

Network coding and spherical buildings

We develop a network coding technique based on flags of subspaces and a corresponding network channel model. To define error correcting codes we introduce a new distance on the flag variety, the Grassmann distance on flags and compare it to the commonly used gallery distance for full flags.