Hypersurfaces with parallel affine curvature tensor R*

• Autorzy: Barbara Opozda , Leopold Verstraelen
• Języki publikacji: EN

Abstrakty

EN

In [OV] we introduced an affine curvature tensor R*. Using it we characterized some types of hypersurfaces in the affine space $ℝ^{n+1}$. In this paper we study hypersurfaces for which R* is parallel relative to the induced connection.

Słowa kluczowe

EN

curvature tensor; induced connection; affine normal

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1999
• Tom: 72
• Numer: 1
• Strony: 25-32

Daty

wydano

1999

otrzymano

1997-12-15

poprawiono

1998-07-13

Twórcy

autor

Barbara Opozda

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

autor

Leopold Verstraelen

• Dept. Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200B B, 3030 Leuven, Belgium

Bibliografia

• [D]₁ R. Deszcz, Pseudosymmetry curvature conditions imposed on the shape operators of hypersurfaces in the affine space, Results Math. 20 (1991), 600-621.
• [D]₂ R. Deszcz, Certain curvature characterizations of affine hypersurfaces, Colloq. Math. 63 (1992), 21-39.
• [NS] K. Nomizu and T. Sasaki, Affine Differential Geometry, Cambridge Univ. Press, 1994.
• [O] B. Opozda, A class of projectively flat surfaces, Math. Z. 219 (1995), 77-92.
• [OS] B. Opozda and T. Sasaki, Surfaces whose images of affine normal are curves, Kyushu Math. J. 49 (1995), 1-10.
• [OV] B. Opozda and L. Verstraelen, On a new curvature tensor in affine differential geometry, in: Geometry and Topology of Submanifolds II, World Sci., 1990, 271-293.
• [VV] P. Verheyen and L. Verstraelen, Locally symmetric affine hypersurfaces, Proc. Amer. Math. Soc. 93 (1985), 101-105.