A global characterization of tubed surfaces in $\mathbb {C}^2$
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- by Michael Bolt PDF
- Proc. Amer. Math. Soc. 138 (2010), 2771-2777 Request permission
Abstract:
Let $M^3\subset \mathbb {C}^2$ be a three times differentiable real hypersurface. The Levi form of $M$ transforms under biholomorphism, and when restricted to the complex tangent space, the skew-Hermitian part of the second fundamental form transforms under Möbius transformations. The surfaces for which these forms are constant multiples of each other were identified in previous work, provided the constant is not unimodular. Here it is proved that if the surface is assumed to be complete and if the constant is unimodular, then the surface is tubed over a strongly convex curve. The converse statement is true, too, and is easily proved.References
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Additional Information
- Michael Bolt
- Affiliation: Department of Mathematics and Statistics, Calvin College, 1740 Knollcrest Circle SE, Grand Rapids, Michigan 49546-4403
- Email: mbolt@calvin.edu
- Received by editor(s): September 18, 2009
- Published electronically: April 8, 2010
- Additional Notes: This is based on work supported by the National Science Foundation under Grant No. DMS-0702939 and by Calvin College through a Calvin Research Fellowship.
- Communicated by: Franc Forstneric
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 2771-2777
- MSC (2010): Primary 32V40; Secondary 53C45
- DOI: https://doi.org/10.1090/S0002-9939-10-10449-3
- MathSciNet review: 2644891