34 citations · 70 across the 14 of their papers we have counts for
15 papers
Complete totally geodesic subsets of the complex hyperbolic plane: an elementary classification
Hugo C. Botós, Carlos H. Grossi
The non-trivial complete totally geodesic submanifolds of the complex hyperbolic plane are the complex geodesics and the real planes. We present two new p…
Quotients of the holomorphic 2-ball and the turnover
Hugo C. Botós, Carlos H. Grossi
We construct two-dimensional families of complex hyperbolic structures on disc orbibundles over the sphere with three cone points. This contrasts with the previously known examples…
Information geometric approach to mixed state quantum estimation
Gabriel F. Magno, Carlos H. Grossi, Gerardo Adesso +1
Information geometry promotes an investigation of the geometric structure of statistical manifolds, providing a series of elucidations in various areas of scientific knowledge. In…
On the geometry of the kinematic space in special relativity
Rafael Ferreira, João dos Reis Junior, Carlos H. Grossi
The classifying space of inertial reference frames in special relativity is naturally hyperbolic. There is a remarkable interplay between central elements of hyperbolic geometry an…
Special elliptic isometries, relative SU(2,1)-character varieties, and bendings
Felipe A. Franco, Carlos H. Grossi
We study relations between special elliptic isometries in the complex hyperbolic plane. Relations of lengths 2, 3, and 4 are fully classified. Some relative SU(2,1)-character varie…
Seidel's conjectures in hyperbolic 3-space
Omar Chavez Cussy, Carlos H. Grossi
We prove, in the case of hyperbolic 3-space, a couple of conjectures raised by J. J. Seidel in "On the volume of a hyperbolic simplex", Stud. Sci. Math. Hung. 21, 243-249, 1986. Th…
Hyperbolic 2-spheres with cone singularities
Sasha Anan'in, Carlos H. Grossi, Jaejeong Lee +1
We study the space of hyperbolic 2-spheres with cone points of prescribed apex curvatures and some related spaces. For ,…
Poincaré's polyhedron theorem for cocompact groups in dimension 4
Sasha Anan'in, Carlos H. Grossi, Júlio C. C. da Silva
We prove a version of Poincaré's polyhedron theorem whose requirements are as local as possible. New techniques such as the use of discrete groupoids of isometries are introduced.…
Basic coordinate-free non-Euclidean geometry
Sasha Anan'in, Carlos H. Grossi
These 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.
Differential geometry of grassmannians and Plucker map
Sasha Anan'in, Carlos H. Grossi
Using the Plucker map between grassmannians, we study basic aspects of classic grassmannian geometries. For `hyperbolic' grassmannian geometries, we prove some facts (for instance,…
Grassmannians and conformal structure on absolutes
Sasha Anan'in, Eduardo C. Bento Goncalves, Carlos H. Grossi
We study grassmannians associated with a linear space with a nondegenerate hermitian form. The geometry of these grassmannians allows us to explain the relation between a (pseudo-)…
Yet Another Poincare's Polyhedron Theorem
Sasha Anan'in, Carlos H. Grossi
Poincaré's Polyhedron Theorem is a widely known valuable tool in constructing manifolds endowed with a prescribed geometric structure. It is one of the few criteria providing discr…
On the type of triangle groups
Carlos H. Grossi
We prove a conjecture of R. Schwartz about the type of some complex hyperbolic triangle groups.
Coordinate-free classic geometries
Sasha Anan'in, Carlos H. Grossi
This paper is devoted to a coordinate-free approach to several classic geometries such as hyperbolic (real, complex, quaternionic), elliptic (spherical, Fubini-Study), and lorentzi…
Complex Hyperbolic Structures on Disc Bundles over Surfaces
Sasha Anan'in, Carlos H. Grossi, Nikolay Gusevskii
We study complex hyperbolic disc bundles over closed orientable surfaces that arise from discrete and faithful representations H_n->PU(2,1), where H_n is the fundamental group of t…