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On rigidity of affine surfaces

Author: Barbara Opozda
Journal: Proc. Amer. Math. Soc. 124 (1996), 2175-2184
MSC (1991): Primary 53A15; Secondary 53B05
MathSciNet review: 1363435
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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.

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Additional Information

Barbara Opozda
Affiliation: Instytut Matematyki, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Keywords: Blaschke surface, metric compatible with connection
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
Article copyright: © Copyright 1996 American Mathematical Society