On some distance function on the Engel group

Greshnov Aleksandr Valer'evich

0000-0002-1218-2767

Scopus Author ID: 6506409279

Researcher ID: 14988

1. Novosibirsk state university, Novosibirsk, Russia

greshnov@math.nsc.ru

On the canonical Engel group $\Bbb E_{\alpha,\beta}$ the properties of the cc-shortest, which are uplift of the cc-shortest of canonical first Heisenberg group $\Bbb H^1_{\alpha}$, are studied. Based on the results obtained on the canonical Engel group $\Bbb E_{\alpha,\beta}$, special (q_1,q_2)-quasimetrics $d_{cq}$ are introduced, which are not analogous to the Box-quasimetrics, and their properties are studied. It is proved that for a sufficiently wide set of parameters $\alpha$, $\beta$ (q_1,q_2)-quasimetrics $d_{cq}$ are not (1,q)-quasimetrics.

УДК 517

Keywords: (q_1,q_2)-quasimetric, Box-quasimetric, Heisenberg group, Engel group, Carnot--Caratheodory metric, сc-shortest.