
slies sidhaantham (deferential jyamiti)

deferential jyamithiyil, slies sidhaantham iprakaaram prasthaavikkunnu "m" ennathil eathenkilum "x" ennathinu, oru lye group "g" defiomorphisangalaayi pravartthikkunna oru manifold "m" nalkumbol, mapp formula _ 1 formula _ 3 leeii formula _ 2 (poojya vibhaagamaayi kaanunnu) yude oru asthiramaaya ayalpakkathekku vyaapikkunnu, angane athu ayalpakkathil ninnu athinte chithrathilekkulla oru ekviveriyant defiomorphisathe nirvachikkunnu, athil "x" nte bhramanapatham adangiyirikkunnu.
g" othungunnathum pravartthanam swathanthravumaayirikkumbol kvoshant formula _ 4 oru manifold ghadanaye amgeekarikkunnu enna vasthuthayude thelivaanu sidhaanthathinte pradhana prayogam.
beejaganita jyamithiyil, slies sidhaanthathinu oru analog undu; ithine loonayude slies sidhaantham ennu vilikkunnu.
jii" othungumbol thelivu enna ashayam.
g" compact aayathinal, oru invariyant metrik undu; i.iii.g" isometrikalaayi pravartthikkunnu. eee metrik upayogichu oru tubular ayalpakkathinte nilanilppinte saadhaarana thelivu oraal sweekarikkunnu.