The convex and concave decomposition of manifolds with real projective structures
The geometry of dented pentagram maps
We propose a new family of natural generalizations of the pentagram map from 2D to higher dimensions and prove their integrability on generic twisted and closed polygons. In dimension there are such generalizations called dented pentagram maps, and we describe their geometry, continuous limit, and Lax representations with a spectral parameter. We prove algebraic-geometric integrability of the dented pentagram maps in the 3D case and compare the dimensions of invariant tori for the dented maps...
The polar curve of a foliation on
We study some properties of the polar curve associated to a singular holomorphic foliation on the complex projective plane . We prove that, for a generic center , the curve is irreducible and its singular points are exactly the singular points of with vanishing linear part. We also obtain upper bounds for the algebraic multiplicities of the singularities of and for its number of radial singularities.
Two models of non-Euclidean spaces generated by associative algebras
Tzitzeica-Bäcklund theorems.