Sasha Anan'in
Basic coordinate-free non-Euclidean geometry.
Tue, 07/05/2011 - 15:01 — SomNambulAuthors: Sasha Anan'in, Carlos H. Grossi
Subjects: Differential Geometry
AbstractThese lecture notes are based on [arXiv: math/0702714, 0907.4469, 0907.4470].
We introduce and study basic aspects of non-Euclidean geometries from a
coordinate-free viewpoint.Coordinate-Free Classic Geometries I. Projective Case.
Fri, 10/30/2009 - 16:01 — SomNambulAuthors: Sasha Anan'in, Carlos H. Grossi
Subjects: Differential Geometry
AbstractThis is the first of a series of papers dedicated to a coordinate-free
approach to several classic geometries such as hyperbolic (real, complex,
quaternionic), elliptic (spherical, Fubini-Study), and lorentzian ones. These
geometries carry a certain simple structure that is in some sense stronger than
the riemannian one. Their basic geometrical objects have linear nature. Such
objects provide natural compactifications of commonly studied geometries. The
usual riemannian concepts are easily derivable from the strong structure and
thus gain their coordinate-free form.Coordinate-free Classic Geometries II. Conformal Structure.
Fri, 10/30/2009 - 16:01 — SomNambulAuthors: Sasha Anan'in, Carlos H. Grossi, Eduardo C. Bento Goncalves
Subjects: Differential Geometry
AbstractWe study grassmannian classic geometries in the spirit of the previous paper.
The interrelation between a (pseudo-)riemannian projective classic geometry and
the conformal structure on its absolute is explained.Yet Another Poincare's Polyhedron Theorem.
Tue, 09/01/2009 - 12:47 — SomNambulAuthors: Sasha Anan'in, Carlos H. Grossi
Subjects: Geometric Topology
AbstractThis work contains a new version of Poincare's Polyhedron Theorem that also
suits geometries of nonconstant curvature lacking the help from typical
convexity arguments. Most conditions of the theorem, being as local as
possible, are easy to verify in practice.
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