Abstract
The topology of the set of singular support hyperplanes and hyperspheres to a smooth submanifold in Euclidean space is studied. As a corollary, some relations between differential-geometric characteristics of a manifold are obtained. In particular, if a simple closed embedded generic curve in a plane has C global vertices (where the curvature circles are support circles to the curve) and T support circles touching the curve at three points, then C − T = 4. Similar invariants are also obtained for submanifolds in higher-dimensional spaces.
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References
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© 1997 Birkhäuser Boston
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Sedykh, V.D. (1997). Invariants of submanifolds in Euclidean space. In: Arnold, V.I., Gelfand, I.M., Retakh, V.S., Smirnov, M. (eds) The Arnold-Gelfand Mathematical Seminars. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4122-5_19
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DOI: https://doi.org/10.1007/978-1-4612-4122-5_19
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8663-9
Online ISBN: 978-1-4612-4122-5
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