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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Projectively flat surfaces in $ {\bf A}\sp 3$


Author: Fabio Podestà
Journal: Proc. Amer. Math. Soc. 119 (1993), 255-260
MSC: Primary 53B05; Secondary 53A15
MathSciNet review: 1169045
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Abstract: We consider a nondegenerate immersion $ f:{M^2} \to {\mathbb{A}^3}$ of an orientable $ 2$-dimensional manifold $ {M^2}$ together with the Blaschke connection $ \nabla $ induced on $ {M^2}$; this work is aimed at studying locally convex surfaces whose Blaschke connection is projectively flat, reducing the problem of their classification to a system of PDE's. In particular we can prove the existence of locally convex projectively flat surfaces which are not locally symmetric.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1169045-7
PII: S 0002-9939(1993)1169045-7
Article copyright: © Copyright 1993 American Mathematical Society