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. We prove that k-harmonic manifolds are necessarily 2-stein and show that locally symmetr...

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Veröffentlicht in:	Advances in geometry 2006-01, Vol.6 (1), p.53-70
Hauptverfasser:	Nicolodi, Lorenzo, Vanhecke, Lieven
Format:	Artikel
Sprache:	eng
Schlagworte:	Damek-Ricci spaces Einstein spaces geodesic spheres Harmonic spaces k-harmonic spaces k-stein spaces shape operator two-point homogeneous spaces
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