Integral geometry of real surfaces in complex projective spaces

Biquaternions Lie Algebra and Complex-Projective Spaces

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Spaces of algebraic maps from real projective spaces into complex projective spaces

We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. It was already shown in [1] that the inclusion of the first space into the second one is a homotopy equivalence. In this paper we prove that the homotopy types of the terms of the natural ‘degree’ filtration approximate closer and closer the homotopy type of the space o...

Pseudo Ricci symmetric real hypersurfaces of a complex projective space

Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.

Prehomogenous spaces and projective geometry

Packings in real projective spaces

This paper applies techniques from algebraic and differential geometry to determine how to best pack points in real projective spaces. We present a computer-assisted proof of the optimality of a particular 6-packing in RP, we introduce a linear-time constant-factor approximation algorithm for packing in the so-called Gerzon range, and we provide local optimality certificates for two infinite fa...