# Geometry of extended Bianchi–Cartan–Vranceanu spaces

@article{Ferrndez2018GeometryOE,
title={Geometry of extended Bianchi–Cartan–Vranceanu spaces},
author={Angel Ferr{\'a}ndez and Antonio Mart{\'i}nez Naveira and Ana D. Tarr{\'i}o},
journal={Revista de la Real Academia de Ciencias Exactas, F{\'i}sicas y Naturales. Serie A. Matem{\'a}ticas},
year={2018},
volume={113},
pages={1515-1532}
}
• Published 31 January 2018
• Mathematics
• Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
The differential geometry of three-dimensional Bianchi, Cartan and Vranceanu (BCV) spaces is well known. We introduce the extended Bianchi, Cartan and Vranceanu (EBCV) spaces as a natural seven dimensional generalization of BCV spaces and study some of their main geometric properties, such as the Levi-Civita connection, Ricci curvatures, Killing fields and geodesics.
1 Citations
The Real Jacobi Group Revisited
The real Jacobi group $G^J_1(\mathbb{R})$, defined as the semi-direct product of the group ${\rm SL}(2,\mathbb{R})$ with the Heisenberg group $H_1$, is embedded in a $4\times 4$ matrix realisation ofExpand

#### References

SHOWING 1-10 OF 29 REFERENCES
Higher Order Parallel Surfaces in Bianchi–Cartan–Vranceanu Spaces
Abstract.We give a full classification of higher order parallel surfaces in three-dimensional homogeneous spaces with four-dimensional isometry group, i.e., in the so-called Bianchi–Cartan–VranceanuExpand
Surfaces with parallel second fundamental form in Bianchi-Cartan-Vranceanu spaces
• Mathematics
• 2002
We give a complete classification of surfaces with parallel second fundamental form in 3-dimensional Bianchi-Cartan-Vranceanu spaces.
A Tour of Subriemannian Geometries, Their Geodesics and Applications
Geodesics in subriemannian manifolds: Dido meets Heisenberg Chow's theorem: Getting from A to B A remarkable horizontal curve Curvature and nilpotentization Singular curves and geodesics A zoo ofExpand
Sugli spazi omogenei di dimensione tre SO(2) - isotropi
In this thesis we studied some problems from the theory of the submanifolds of the three-dimensional Riemannian manifolds. Our intention is to evaluate which properties of the submanifolds dependExpand
Homogeneous Structures on Riemannian Manifolds
• Mathematics
• 1983
1. The theorem of Ambrose and Singer 2. Homogeneous Riemannian structures 3. The eight classes of homogeneous structures 4. Homogeneous structures on surfaces 5. Homogeneous structures of type T1 6.Expand
On the Three-Dimensional Homogenous SO(2)-Isotropic Riemannian Manifolds
• Mathematics
• 2010
On the Three-Dimensional Homogenous SO(2)-Isotropic Riemannian Manifolds In this paper we consider some properties of the three-dimensional homogenous SO(2)-isotropic Riemannian manifolds. InExpand
On the Three-Dimensional Spaces Which Admit a Continuous Group of Motions
namely the law by which we measure infinitesimal arclengths in the space Sn, from which the law of measure for finite arclengths follows. We consider n independent real variables x1, x2, . . . , xnExpand
Sub-Riemannian Geometry: General Theory and Examples
• Mathematics
• 2009
Part I. General Theory: 1. Introductory chapter 2. Basic properties 3. Horizontal connectivity 4. Hamilton-Jacobi theory 5. Hamiltonian formalism 6. Lagrangian formalism 7. Connections onExpand
Quaternionic contact normal coordinates
This paper constructs a family of coordinate systems about a point on a quaternionic contact manifold, called quaternionic contact pseudohermitian normal coordinates. Once defined, conformalExpand
Cosmic Topology
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multi-- rather than simply--connected. We review the main mathematical properties ofExpand