ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 053 Haroutounian, Samuel, Armenian State Pedagogical University, Armenia On geometry of m-pairs manifold in projective space RP^{n} One of the main results of the theory of n-multiple integrals depending on n parameters affirms that such integral under some natural condition invariantly generates the structure of Rashevsky space (pseudoriemannian space with the metric of half index) on 2n-dimensional double fibre manifold M, associated to integral. The family of m-pairs (m-plane – (n − m − 1)-plane) in n-dimensional real projective space RP^{n} has more rich geometry then RP^{n} : M is 2(n−m)(m+ 1)-dimensional Rashevsky space and moreover Einstein space. The system of differential equations defining this structure on the double fibre manifold associated to the multiple integral depending on parameters is studied.