Title: Geometry of generalized heisenberg groups and their damek-ricci harmonic extensions
Authors: Berndt, J ×
Tricerri, F
Vanhecke, Lieven #
Issue Date: 1994
Publisher: Gauthier-villars
Series Title: Comptes rendus de l academie des sciences serie i-mathematique vol:318 issue:5 pages:471-476
Abstract: It is proved that on any generalized Heisenberg group the principal curvatures of small geodesic spheres are invariant by local geodesic symmetries and the spectrum of the Jacobi operator is constant along geodesics. A method to compute the Jacobi fields on generalized Heisenberg groups is presented. Furthermore it is proved that a Damek-Ricci harmonic space is symmetric if and only if the spectrum of the Jacobi operator is constant along geodesics, or equivalently, if and only if along each geodesic the Jacobi operator is diagonalizable by a parallel orthonormal frame field.
ISSN: 0764-4442
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Mathematics - miscellaneous
× corresponding author
# (joint) last author

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