What question did this study set out to answer?

The study explores the conditions under which the connected isometry group of non-symmetric Damek-Ricci spaces has a surjective exponential map.

March 29, 2026Open Access

On the Exponential Map of the Connected Isometry Group of a Damek-Ricci Space

Puntos clave

The study explores the conditions under which the connected isometry group of non-symmetric Damek-Ricci spaces has a surjective exponential map.
Proved conditions for the surjectivity of the exponential map.
Analyzed the dimension of the center of the associated Heisenberg type algebra.
Extended previous findings related to classical symmetric spaces.
The exponential map is surjective if the center of the Heisenberg algebra has a dimension of 5 or less.
This result generalizes previous work on symmetric spaces to a broader class of spaces.

Resumen

We prove that the connected isometry group of a non symmetric (non compact) irreducible Damek-Ricci space has a surjective exponential map if and only if the center of the associated Heisenberg type algebra has dimension less than or equal to 5.This result is analogous to (and extends) the results proved by the second author concerning the exponential map of the connected isometry group of an irreducible, rank one, classical, symmetric space of non compact type and that of D. Djokovic and N. Thang On the exponential group of almost simple real algebraic groups, J. Lie Theory 5 (1996) 275-291 in the case of the Cayley plane to all irreducible non compact DR spaces.

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