Locally convex immersed surfaces with flat Euclidean boundary
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O186.12

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    Abstract:

    In affine differential geometry, the geometric and topological behavior of locally strongly (uniformly) convex immersed surfaces(hypersufaces) are very complicated, so are their Euclidean boundaries. In this paper we construct a new locally strongly convex ( but not globally convex) immersed surface(hypersurfaces) with flat Euclidean boundary in $\mathbb{R}^{n+1},(n=2,3)$ , respectively, which are different from an existing conclusion.

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Cite this article as: WANG Bao-Fu. Locally convex immersed surfaces with flat Euclidean boundary [J]. J Sichuan Univ: Nat Sci Ed, 2020, 57: 7.

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History
  • Received:January 31,2019
  • Revised:June 11,2019
  • Adopted:June 13,2019
  • Online: January 10,2020
  • Published: