Almost-Riemannian Structures on nonnilpotent, solvable 3D Lie groups
نویسندگان
چکیده
In this paper we study Almost-Riemannian Structures (ARS) on the class of nonnilpotent, solvable, conneted 3D Lie groups. The nice structures present in such groups allow us to show that singular locus ARSs are always embedded submanifolds.
منابع مشابه
Sub-Riemannian structures on 3D Lie groups
We give a complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. As a corollary we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups SL(2) and A(R)× S, where A(R) denotes the group of orientation preserving affine maps on the real line.
متن کاملAlmost-Riemannian Geometry on Lie Groups
A simple Almost-Riemannian Structure on a Lie group G is defined by a linear vector field (that is an infinitesimal automorphism) and dim(G) − 1 left-invariant ones. We state results about the singular locus, the abnormal extremals and the desingularization of such ARS’s, and these results are illustrated by examples on the 2D affine and the Heisenberg groups. These ARS’s are extended in two wa...
متن کاملAbelian Complex Structures on Solvable Lie Algebras
We obtain a characterization of the Lie algebras admitting abelian complex structures in terms of certain affine Lie algebras aff(A), where A is a commutative algebra.
متن کاملNovikov Structures on Solvable Lie Algebras
We study Novikov algebras and Novikov structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov structure must be solvable. Conversely we present an example of a nilpotent 2-step solvable Lie algebra without any Novikov structure. We construct Novikov structures on certain Lie algebras via classical r-matrices and via extensions. In the latter case we lift No...
متن کاملEinstein structures on four-dimensional nutral Lie groups
When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2023
ISSN: ['1879-1662', '0393-0440']
DOI: https://doi.org/10.1016/j.geomphys.2023.104922