The magid-ryan conjecture for 4-dimensional affine spheres |
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| Authors: | Els Bergen Esther Ramakers Luc Vrancken |
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| Institution: | 1. Fachbereich Mathematik, Sekr. MA 8-3, Technische Universit?t Berlin, Strasse des 17 Juni 135, D-10623, Berlin, Germany
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| Abstract: | In this paper we prove the Magid-Ryan conjecture for 4-dimensional affine hyperspheres in R5. This conjecture states that every affine hypersphere with non-zero Pick invariant and constant sectional curvature is affinely
equivalent with either (x
1
2
±x
2
2
)(x
3
2
±x
4
2
...(x
2m−1
2
±x
2m
2
) = 1 or (x
1
2
±x
2
2
(x
3
2
±x
4
2
)...(x
2m−1
2
±x
2m
2
)x
2m+1 = 1 where the dimensionn satisfiesn = 2m orn =2m + 1. This conjecture was proved in 11] in case the metric is positive definite and in 2] in case the metric is Lorentzian. |
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| Keywords: | |
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