Article
Licensed
Unlicensed
Requires Authentication
Carnot spaces and the k-stein condition
-
María J Druetta
Published/Copyright:
August 10, 2006
Abstract
A riemannian manifold M with associated Jacobi operators RX (RXY = R(Y, X) X), X in TM, is said to be k-stein, k ≥ 1, if there exists a function μk on M such that tr(RkX) = μk|X|2k for all X in TM. We study the k-stein condition on Lie groups of Iwasawa type and in particular in those which are Carnot spaces. We show that a Carnot space which is k-stein for some k > 1 is necessarily a Damek–Ricci space; Damek–Ricci spaces are Einstein and 2-stein and they are not k-stein for any k ≥ 3, unless they are symmetric. Moreover, we show that a harmonic Lie group of Iwasawa type which is 3-stein is a symmetric space of noncompact type and rank one.
Key words: Lie group of Iwasawa type; Carnot spaces; k-stein condition; rank one symmetric spaces; Damek–Ricci spaces; Harmonic spaces
Received: 2004-08-03
Revised: 2005-03-01
Published Online: 2006-08-10
Published in Print: 2006-07-01
© Walter de Gruyter
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- On the surjectivity of the canonical Gaussian map for multiple coverings
- A classification of 4-dimensional elation Laguerre planes of group dimension 10
- Completely regular ovals
- Symmetry and the farthest point mapping on convex surfaces
- Certain Roman and flock generalized quadrangles have nonisomorphic elation groups
- Similarity structures on the torus and the Klein bottle via triangulations
- On Euclidean designs
- Carnot spaces and the k-stein condition
- Simplicity of the universal quotient bundle restricted to congruences of lines in ℙ3
- Entropy of the geodesic flow for metric spaces and Bruhat–Tits buildings
Keywords for this article
Lie group of Iwasawa type;
Carnot spaces;
k-stein condition;
rank one symmetric spaces;
Damek–Ricci spaces;
Harmonic spaces
Articles in the same Issue
- On the surjectivity of the canonical Gaussian map for multiple coverings
- A classification of 4-dimensional elation Laguerre planes of group dimension 10
- Completely regular ovals
- Symmetry and the farthest point mapping on convex surfaces
- Certain Roman and flock generalized quadrangles have nonisomorphic elation groups
- Similarity structures on the torus and the Klein bottle via triangulations
- On Euclidean designs
- Carnot spaces and the k-stein condition
- Simplicity of the universal quotient bundle restricted to congruences of lines in ℙ3
- Entropy of the geodesic flow for metric spaces and Bruhat–Tits buildings
