A. A. Akopyan, A. V. Levichev, “On $\mathrm{SO}(3,3)$ as the projective group of the space $\mathrm{SO}(3)$”, Zap. Nauchn. Sem. POMI, 2018, Volume 476,Pages 5

On $\mathrm{SO}(3,3)$ as the projective group of the space $\mathrm{SO}(3)$

A. A. Akopyan^a, A. V. Levichev^b

^a Boston University, 985 Commonwealth Ave., Boston, MA 02215, USA
^b Sobolev Institute of Mathematics, Siberian Division of the Russian Academy of Sciences, 4 Koptiug pr., Novosibirsk, 630090, Russia

Abstract: The fractional linear action of $\mathrm{SO}(3,3)$ on the projective space $\mathrm{SO}(3)$ is proven to be a (globally defined) projective action.

Key words and phrases: $2$-cover of $\mathrm{SO}(3,3)$ by $\mathrm{SL}(4)$, fractional linear action of $\mathrm{SO}(3,3)$ on $\mathrm{SO}(3)$, bi-invariant metrics, geodesics, $2$-cover of $S^1\times \mathrm{SO}(3)$ by Segal's compact cosmos $\mathrm{UU}(2)$.

UDC: 514.14

Received: 03.11.2018

Language: English