Evgeniy Rogozinnikov

Gruppy Preobrazovaniy Krivykh: Krivye Vdol' Mnogoobraziy I Ikh Obobshcheniya Evgeniy Rogozinnikov Russian edition

Izvestno, chto mnozhestva vozmozhnykh sostoyaniy razlichnykh evolyutsioniruyushchikh sistem mozhno rassmatrivat' kak gladkie mnogoobraziya. Nepreryvnaya evolyutsiya rassmatrivaemoy sistemy predstavlyaet soboy krivuyu vdol' etogo mnogoobraziya. S matematicheskoy tochki zreniya krivye na razlichnogo roda geometricheskikh ob"ektakh yavlyayutsya klassicheskim ob"ektom issledovaniy. Gruppy preobrazovaniy geometricheskikh ob"ektov yavlyayutsya vazhneyshimi i klassicheskimi proizvodnymi strukturami, v terminakh kotorykh osushchestvlyaetsya klassifikatsiya geometricheskikh ob"ektov i provoditsya issledovanie ikh razlichnykh svoystv. Nastoyashchaya monografiya posvyashchena izucheniyu krivykh, a takzhe nekotorykh obobshcheniy etogo ponyatiya, v terminakh ikh grupp preobrazovaniy. Issleduetsya stroenie grupp preobrazovaniy krivykh, rassmatrivayutsya vzaimosvyazi mezhdu geometricheskimi svoystvami krivykh i svoystvami ikh grupp preobrazovaniy, ustanavlivayutsya usloviya, pri kotorykh vozmozhno postroenie krivoy po zadannoy gruppoy preobrazovaniy. Osoboe vnimanie udeleno izucheniyu krivykh vdol' gladkikh mnogoobraziy, poskol'ku takie krivye, a takzhe ikh gruppy dvizheniy yavlyayutsya naibolee vazhnymi s prikladnoy tochki zreniya.