52 research outputs found
Submanifolds with nonparallel first normal bundle revisited
In this paper, we analyze the geometric structure of an Euclidean submanifold
whose osculating spaces form a nonconstant family of proper subspaces of the
same dimension. We prove that if the rate of change of the osculating spaces is
small, then the submanifold must be a (submanifold of a) ruled submanifold of a
very special type. We also give a sharp estimate of the dimension of the
rulings.Comment: 11 pages. Final version. To appear in Pub. Ma
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