ArticleOriginal scientific text
Title
Affine surfaces with parallel shape operators
Authors 1
Affiliations
- Institute of Mathematics, Technical University of Cracow, Warszawska 24, 31-155 Kraków, Poland
Abstract
We study affine nondegenerate Blaschke hypersurfaces whose shape operators are parallel with respect to the induced Blaschke connections. We classify such surfaces and thus give an exact classification of extremal locally symmetric surfaces, first described by F. Dillen.
Keywords
Blaschke structure, affine locally symmetric surface, affine shape operator, equiaffine structure, affine normal field
Bibliography
- F. Dillen, Locally symmetric complex affine hypersurfaces, J. Geom. 33 (1988), 27-38.
- F. Dillen, Equivalence theorems in affine differential geometry, Geom. Dedicata 32 (1989), 81-92.
- M. Magid and K. Nomizu, On affine surfaces whose cubic forms are parallel relative to the affine metric, Proc. Nat. Acad. Sci. U.S.A. 65 (1989), 215-218.
- K. Nomizu, On completeness in affine differential geometry, Geom. Dedicata 20 (1986), 43-49.
- K. Nomizu and U. Pinkall, On the geometry of affine immersions, Math. Z. 195 (1987), 165-178.
- K. Nomizu and U. Pinkall, Cayley surfaces in affine differential geometry, Tôhoku Math. J. 41 (1989), 589-596.
Pages:
179-186
Main language of publication
English
Received
1990-11-21
Accepted
1991-03-26
Published
1992
Exact and natural sciences