Dong-Soo Kim
Abstract
We study hypersurfaces in the Euclidean space with the following property: the tangential part of the position vector has constant length. As a result, we prove that among the connected and complete hypersurfaces in the Euclidean space, only the hypersphere centered at the origin satisfies the property.
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We study hypersurfaces in the Euclidean space with the following property: the tangential part of the position vector has constant length. As a result, we prove that among the connected and complete hypersurfaces in the Euclidean space, only the hypersphere centered at the origin satisfies the property.
Key concepts: Hypersphere, Mathematics, Euclidean space, Property (philosophy), Characterization (materials science), Euclidean geometry, Position (finance), Euclidean distance