Normal curvatures and Euler classes for polyhedral surfaces in $4$-space
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- by Thomas F. Banchoff PDF
- Proc. Amer. Math. Soc. 92 (1984), 593-596 Request permission
Abstract:
Using the approach of singularities of projections into lower dimensional spaces it is possible to define nonintrinsic local curvature quantities at each vertex of a polyhedral surface immersed in $4$-space which add up to the normal Euler number of the immersion. Related uniqueness results for lattice polyhedra have been established by B. Yusin.References
- Thomas Banchoff, Critical points and curvature for embedded polyhedra, J. Differential Geometry 1 (1967), 245–256. MR 225327 —, The normal Euler class of a polyhedral surface in $4$-space (to appear).
- Hassler Whitney, On the topology of differentiable manifolds, Lectures in Topology, University of Michigan Press, Ann Arbor, Mich., 1941, pp. 101–141. MR 0005300
- Boris V. Yusin, A combinatorial formula for the normal Euler class of a lattice $2$-manifold in $4$-space, Proc. Amer. Math. Soc. 92 (1984), no. 4, 578–592. MR 760949, DOI 10.1090/S0002-9939-1984-0760949-8
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 593-596
- MSC: Primary 57Q35; Secondary 53C40, 57R20
- DOI: https://doi.org/10.1090/S0002-9939-1984-0760950-4
- MathSciNet review: 760950