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On harmonic and 2-stein spaces of Iwasawa type

✍ Scribed by Maria J Druetta

Book ID
104358203
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
117 KB
Volume
18
Category
Article
ISSN
0926-2245

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✦ Synopsis

We study geometric properties of solvable metric Lie groups S of Iwasawa type; in particular harmonicity and the 2-stein condition. One restriction we obtain is that harmonic spaces of Iwasawa type have algebraic rank one, that is, the commutator subgroup of S has codimension one.

We show that among Carnot solvmanifolds the only harmonic spaces are the Damek-Ricci spaces. Moreover, this rigidity result remains valid if harmonicity is replaced by the weaker 2-stein condition. As an application, we show that a harmonic Lie group of Iwasawa type with nonsingular 2-step nilpotent commutator subgroup is, up to scaling, a Damek-Ricci space.

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