Last update: 12/02/2021
We are interested in the following problems about submanifolds of hyperbolic spaces:
Construct equivariant minimal hypersurfaces.
Study bisectors, and some related objets, in quaternionic hyperbolic spaces.
Classification of isometries of low dimensional hyperbolic spaces.
Exploit the relative position of totally geodesic submanifolds of real hiperbolic spaces, that is, determine the congruence class of pairs and triples of totally geodesic submanifolds of the hyperbolic space under the action of its isometry group. Moreover, we are interested to study trace fields of complex hyperbolic groups.
We are also interested in the study of isoparametric hypersurfaces of the infinite dimensional Hilbert space.
ORJUELA, JAIME and TOJEIRO, RUY. Umbilical surfaces of products of space forms. Tohoku Math. J. (2) 68 (2016), no. 3, 471--486.
ORJUELA CHAMORRO, J.L.. Complete minimal hypersurfaces in quaternionic hyperbolic space. Geom Dedicata (2014) 172: 47--67.
VILCA RODRÍGUEZ, JOSÉ L., BRANDÃO A., TAUAN. L. and BATISTA, VICTOR M. O.. Principal angles and pairs of totally geodesic submanifolds of the real hyperbolic space (2020).
CHAMORRO, J. L. O.. Isometries of quaternionic hyperbolic line (2020).