Rational approximation of affine coordinate subspaces of Euclidean space

Diophantine Exponents of Affine Subspaces: the Simultaneous Approximation Case

We apply nondivergence estimates for flows on homogeneous spaces to compute Diophantine exponents of affine subspaces of Rn and their nondegenerate submanifolds.

On Principal Angles between Subspaces of Euclidean Space

Robust self-calibration and Euclidean reconstruction via affine approximation

A new approach to self-calibration and Euclidean reconstruction from image sequences is presented. The key idea is to start with the affine camera model as a first approximation to obtain affine 3D structure. It is then upgraded to Euclidean structure and finally, refined by applying the full perspective camera model. All steps in this procedure are described in detail and well-motivated. The m...

Equiangular subspaces in Euclidean spaces

A set of lines through the origin is called equiangular if every pair of lines defines the same angle, and the maximum size of an equiangular set of lines in R was studied extensively for the last 70 years. In this paper, we study analogous questions for k-dimensional subspaces. We discuss natural ways of defining the angle between k-dimensional subspaces and correspondingly study the maximum s...

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...