TY - JOUR

T1 - Riemannian cubics in quadratic matrix Lie groups

AU - Zhang, Erchuan

AU - Noakes, Lyle

PY - 2020/6/15

Y1 - 2020/6/15

N2 - Quadratic matrix Lie groups are subgroups of the general linear group that satisfy a quadratic matrix identity. The main purpose of this paper is to consider Riemannian cubics in quadratic matrix Lie groups with left-invariant metrics. Results for Riemannian cubics in quadratic matrix Lie groups extend those in SO(n) since the group SO(n) with bi-invariant metric is a very special case. By examining Riemannian cubics in SO(2, 1) and SO(3, 1), we find that the so-called null Lie quadratics in so(p,q) (p > 0, q > 0), and even more generally for any quadratic matrix Lie group, can be given in closed forms in terms of Lie quadratics in so(p) and so(q). Further, we present some quantitative analyses of non-null Lie quadratics in so(p,q).

AB - Quadratic matrix Lie groups are subgroups of the general linear group that satisfy a quadratic matrix identity. The main purpose of this paper is to consider Riemannian cubics in quadratic matrix Lie groups with left-invariant metrics. Results for Riemannian cubics in quadratic matrix Lie groups extend those in SO(n) since the group SO(n) with bi-invariant metric is a very special case. By examining Riemannian cubics in SO(2, 1) and SO(3, 1), we find that the so-called null Lie quadratics in so(p,q) (p > 0, q > 0), and even more generally for any quadratic matrix Lie group, can be given in closed forms in terms of Lie quadratics in so(p) and so(q). Further, we present some quantitative analyses of non-null Lie quadratics in so(p,q).

KW - Generalized orthogonal group

KW - Lie quadratic

KW - Quadratic matrix Lie group

KW - Riemannian cubic

KW - Symplectic group

UR - http://www.scopus.com/inward/record.url?scp=85078999328&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2020.125082

DO - 10.1016/j.amc.2020.125082

M3 - Article

AN - SCOPUS:85078999328

VL - 375

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

M1 - 125082

ER -