Research on Differential Geometry of Submanifolds and Hiperbolic Geometry

Principal investigators:

• Jaime Leonardo Orjuela Chamorro (UFBA)

• Tauan Lucas Amaral Brandão (UFBA)

• Victor Mielly Oliveira Batista (UFRPE)

Description

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.

Research Projects

• Bisectors and some related objets in hyperbolic spaces
  Collaborators:   Prof. Jaime Chamorro (UFBA) and Prof. Nikolai Goussevskii (UFMG).
  Our goal is to do a sistematic study of the theory of bissectors in quaternionic hyperbolic spaces.
• Isometries of quaternionic hyperbolic plane
  Collaborators:   Prof. Jaime Chamorro (UFBA) and Prof. Tauan Lucas Amaral Brandão (UFBA).
  Our goal is to do a classification of the isometries of quaternionic hyperbolic plane by studing its complex representations.
• Spliting field for subgroups of SU(n,1)
  Collaborators:   Prof. Tauan Lucas Amaral Brandão (UFBA), Prof. Victor Mielly O. Batista (UFRPE) and Prof. José L. Vilca Rodríguez (USP).
  Our goal is to find conditions for a subgroup of SU(n,1) to be conjugated to a subgroup of SU(n, 1) with entries in a special field, namely a Spliting field.

Our published works

1. ORJUELA, JAIME and TOJEIRO, RUY. Umbilical surfaces of products of space forms. Tohoku Math. J. (2) 68 (2016), no. 3, 471--486.

2. ORJUELA CHAMORRO, J.L.. Complete minimal hypersurfaces in quaternionic hyperbolic space. Geom Dedicata (2014) 172: 47--67.

Our submitted works

1. 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).

Our preprints

1. CHAMORRO, J. L. O.. Isometries of quaternionic hyperbolic line (2020).

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News

• Seminários 2021
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