On rigidity of affine surfaces
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- by Barbara Opozda PDF
- Proc. Amer. Math. Soc. 124 (1996), 2175-2184 Request permission
Abstract:
Rigidity of nondegenerate Blaschke surfaces in $\mathbf {R}^{3}$ is studied. The rigidity criteria are given in terms of $\nabla R$, where $R$ is the curvature of the Blaschke connection $\nabla$. If the rank of $\nabla R$ is 2, then the surface is rigid. If $\nabla R=0$, it is nonrigid. In the case where the rank of $\nabla R$ is 1 there are both rigid and nonrigid surfaces. This case is discussed for various types of surfaces.References
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Additional Information
- Barbara Opozda
- Affiliation: Instytut Matematyki, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
- Email: opozda@im.uj.edu.pl
- Received by editor(s): May 31, 1994
- Additional Notes: The research was supported by the Kambara Fund of Kobe University and the KBN grant 2P30103004.
- Communicated by: Christopher Croke
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2175-2184
- MSC (1991): Primary 53A15; Secondary 53B05
- DOI: https://doi.org/10.1090/S0002-9939-96-03715-X
- MathSciNet review: 1363435