| Abstract: | We consider strongly parabolic, Hilbert submanifolds in Riemannian Hilbert manifolds. We prove that their properties are analogous to the known properties in the finite-dimensional case. The main geometric result consists of Theorem 3: a complete, Riemannian, Hilbert submanifold of nonpositive extrinsic curvature and finite codimension in a Hilbert sphere is a great sphere.Translated from Ukrainskii Geometricheskii Sbornik, No. 33, pp. 91–100, 1990.The author expresses his thanks to Professor A. A. Borisenko for posing the problem and guiding the work. |
