On the geometrical properties of solvable Lie groups
-
Mansour Aghasi
and
Mehri Nasehi
Abstract
In [3] Bozek introduced a class of solvable Lie groups M2n+1. Calvaruso, Kowalski and Marinosci in [9] have studied homogeneous geodesics on these homogeneous spaces with an arbitrary odd dimension. In [1] we have studied some other geometrical properties on these spaces with dimension five. Our aim in this paper is to extend those geometrical properties for an arbitrary odd dimension in both Riemannian and Lorentzian cases. In fact we first obtain all of the descriptions of their homogeneous Lorentzian and Riemannian structures and their types. Then we calculate the energy of an arbitrary left-invariant vector field X on these spaces and in the Lorentzian case we prove that no left-invariant unit time-like vector fields on these spaces are critical points for the space-like energy. There is also a proof of non-existence of invariant contact structures and left-invariant Ricci solitons on these homogeneous spaces.
© 2015 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Danzer’s configuration revisited
- Sasaki manifolds with positive transverse orthogonal bisectional curvature
- Real open books and real contact structures
- Locally Monge–Ampère parabolic foliations
- Gradient estimates for the heat equation under the Ricci-harmonic map flow
- The Log-Convex Density Conjecture and vertical surface area in warped products
- Further properties of the Bergman spaces of slice regular functions
- Constructions of complete sets
- The Euclidean distortion of generalized polygons
- On the geometrical properties of solvable Lie groups
- Another proof of the Beckman–Quarles theorem
Articles in the same Issue
- Frontmatter
- Danzer’s configuration revisited
- Sasaki manifolds with positive transverse orthogonal bisectional curvature
- Real open books and real contact structures
- Locally Monge–Ampère parabolic foliations
- Gradient estimates for the heat equation under the Ricci-harmonic map flow
- The Log-Convex Density Conjecture and vertical surface area in warped products
- Further properties of the Bergman spaces of slice regular functions
- Constructions of complete sets
- The Euclidean distortion of generalized polygons
- On the geometrical properties of solvable Lie groups
- Another proof of the Beckman–Quarles theorem
