Geometriya mnogoobraziya $m$-ploskostej ellipticheskogo $n$-prostranstva

Al'fiya Shabaeva-Masagutova

Abstract: Izuchaetsya grassmanovo mnogoobrazie $G_{n,m}^s$ $m$-ploskostej ellipticheskogo $n$-prostranstva $S_n$ v ego invariantnoj rimanovoj metrike. Dayutsya novye, bolee prostye dokazatel'stva teorem o geodezicheskih etogo mnogoobraziya ($m$-gelikoidah), o vpolne geodezicheskih podmnogoobraziyah etogo mnogoobraziya, o ego derivacionnyh formulah i tenzore krivizny. V chastnosti, rassmatrivayutsya psevdokongruencii Kartana, paratakticheskie kongruencii i paratakticheskie $m$-gelikoidy. Pokazyvaetsya, chto $m$-puchki, prohodyawie cherez $m$-ploskost', opredelyayut metricheskuyu segreanu v beskonechno udalennoj giperploskosti kasatel,nogo $(m+1)(n-m)$-prostranstva mnogoobraziya $G_{n,m}^s$. Derivacionnye formuly pozvol{yayu}t izuchat, differencial,nuyu geometriyu semejstv $m$-ploskostej.

Classification (MSC2000): 51C35

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