34 citations · 70 across the 14 of their papers we have counts for
8 papers · 1 filter
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…
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…
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-)…
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…