Title: The geometry of k-harmonic manifolds
Authors: Nicolodi, L ×
Vanhecke, Lieven #
Issue Date: 2006
Publisher: Walter de gruyter & co
Series Title: Advances in geometry vol:6 issue:1 pages:53-70
Abstract: 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 symmetric manifolds which are k-harmonic for one k, are k-harmonic for all k. We then establish some results relating the harmonic and k-harmonic conditions for the class of non-compact harmonic non-symmetric spaces constructed by Damek and Ricci. We also discuss other notions of k-harmonicity and the problem of their equivalence.
ISSN: 1615-715X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Mathematics - miscellaneous
× corresponding author
# (joint) last author

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