Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] Katsumi Nomizu, Recent results in affine differential geometry—an introduction and a survey, Geometry and global analysis (Sendai, 1993) Tohoku Univ., Sendai, 1993, pp. 351–357. MR 1361200
  • [2] Katsumi Nomizu and Barbara Opozda, On normal and conormal maps for affine hypersurfaces, Tohoku Math. J. (2) 44 (1992), no. 3, 425–431. MR 1176082,
  • [3] B. Opozda and L. Verstraelen, On a new curvature tensor in affine differential geometry, Geometry and Topology of Submanifolds. II, Avignon, May 1988.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53B05, 53A15

Retrieve articles in all journals with MSC: 53B05, 53A15

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society