Abstract
The notion of contact number \({\mathfrak c}_\#(M)\) of a Euclidean submanifold was introduced in an earlier article (Proc. Edinb. Math. Soc. 47:69–100, 2004) as the highest order of contact of geodesics and normal sections on the submanifold. It was proved in (Proc. Edinb. Math. Soc. 47:69–100, 2004) that the contact number relates closely with the notions of isotropic submanifolds and holomorphic curves. One important problem concerning contact number is to construct Euclidean submanifolds with high contact number. The purpose of this article is thus to construct Euclidean surfaces with high contact number and to provide simple geometric characterization of such surfaces.
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Mathematics Subject Classification (2000) Primary 53C40, 53A10 Secondary 53B25, 53C42
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Chen, BY. Surfaces with high contact number and their characterization. Annali di Matematica 185, 555–576 (2006). https://doi.org/10.1007/s10231-005-0169-1
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DOI: https://doi.org/10.1007/s10231-005-0169-1