The Contact Number of a Euclidean Submanifold
نویسندگان
چکیده
We introduce an invariant, called the contact number, associated with each Euclidean submanifold. We show that this invariant is, surprisingly, closely related to the notions of isotropic submanifolds and holomorphic curves. We are able to establish a simple criterion for a submanifold to have any given contact number. Moreover, we completely classify codimension-2 submanifolds with contact number 3. We also study surfaces in E6 with contact number 4. As an immediate consequence, we obtain the first explicit examples of non-spherical pseudo-umbilical surfaces in Euclidean spaces.
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