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Riemannian Hilbert submanifolds of nonpositive extrinsic curvature

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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.

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Authors
  1. S. I. Okrut
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Additional information

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.

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Okrut, S.I. Riemannian Hilbert submanifolds of nonpositive extrinsic curvature. J Math Sci 53, 526–532 (1991). https://doi.org/10.1007/BF01109656

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  • DOI: https://doi.org/10.1007/BF01109656

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