▁space ▁of ▁a ▁" sym met ry " ▁that ▁is ▁invol utive , ▁leaves ▁the ▁point ▁fixed , ▁and ▁pres erves ▁distances . ▁The ▁unexpected ▁fact ▁discovered ▁by ▁Cart an ▁is ▁that ▁it ▁is ▁possible ▁to ▁give ▁a ▁complete ▁description ▁of ▁these ▁spaces ▁by ▁means ▁of ▁the ▁classification ▁of ▁the ▁simple ▁Lie ▁groups ; ▁it ▁should ▁therefore ▁not ▁be ▁surprising ▁that ▁in ▁various ▁areas ▁of ▁mathematics , ▁such ▁as ▁autom orph ic ▁functions ▁and ▁analyt ic ▁number ▁theory ▁( app ar ently ▁far ▁removed ▁from ▁differential ▁geometry ), ▁these ▁spaces ▁are ▁playing ▁a ▁part ▁that ▁is ▁becoming ▁increasing ly ▁important . ▁ ▁Altern ative ▁theory ▁to ▁general ▁relativ ity ▁ ▁Cart an ▁created ▁a ▁compet itor ▁theory ▁of ▁gravity ▁also ▁Ein stein – Cart an ▁theory . ▁ ▁Publications ▁Cart an ' s ▁papers ▁have ▁been ▁collected ▁in ▁his ▁O e uv res ▁compl ètes , ▁ 6 ▁vol s . ▁( Par is , ▁ 1 9 5 2 – 1 9 5 5 ). ▁Two ▁excellent ▁ob itu ary ▁not ices ▁are ▁S . ▁S . ▁Ch ern ▁and ▁C . ▁Che val ley , ▁in ▁Bul letin ▁of ▁the ▁American ▁Mathemat ical ▁Society , ▁ 5 8 ▁( 1 9 5 2 ); ▁and ▁J . ▁H . ▁C . ▁White head , ▁in ▁Ob itu ary ▁Notices ▁of ▁the ▁Royal ▁Society ▁( 1 9 5 2 ). ▁ ▁Le ç ons ▁sur ▁les ▁invari ants ▁int ég ra ux , ▁Hermann , ▁Paris , ▁ 1 9 2 2