Affine surfaces with parallel shape operators

• Autorzy: Włodzimierz Jelonek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Blaschke structure; affine locally symmetric surface; affine shape operator; equiaffine structure; affine normal field

Kategorie tematyczne

• 53A15: Affine differential geometry

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991-1992
• Tom: 56
• Numer: 2
• Strony: 179-186

Daty

wydano

1992

otrzymano

1990-11-21

poprawiono

1991-03-26

Twórcy

autor

Włodzimierz Jelonek

• Institute of Mathematics, Technical University of Cracow, Warszawska 24, 31-155 Kraków, Poland

Bibliografia

• [1] F. Dillen, Locally symmetric complex affine hypersurfaces, J. Geom. 33 (1988), 27-38.
• [2] F. Dillen, Equivalence theorems in affine differential geometry, Geom. Dedicata 32 (1989), 81-92.
• [3] 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.
• [4] K. Nomizu, On completeness in affine differential geometry, Geom. Dedicata 20 (1986), 43-49.
• [5] K. Nomizu and U. Pinkall, On the geometry of affine immersions, Math. Z. 195 (1987), 165-178.
• [6] K. Nomizu and U. Pinkall, Cayley surfaces in affine differential geometry, Tôhoku Math. J. 41 (1989), 589-596.