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Items for "Harmonic spaces"

The geometry of k-harmonic manifolds

An n-dimensional Riemannian manifold is called k-harmonic for some integer k, 1 ≤ k ≤ n - 1, if the k-th elementary symmetric functions of the principal curvatures of small geodesic spheres are radial functions...

Keywords: Harmonic spaces, k-harmonic spaces, Einstein spaces, k-stein spaces, geodesic spheres, shape operator, two-point homogeneous spaces, Damek-Ricci spaces

01/2006 | Advances in Geometry, Walter de Gruyter
Carnot spaces and the k-stein condition

A riemannian manifold M with associated Jacobi operators RX (RX Y = 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...

Keywords: Lie group of Iwasawa type, Carnot spaces, k-stein condition, rank one symmetric spaces, DamekRicci spaces, Harmonic spaces

07/2006 | Advances in Geometry, Walter de Gruyter