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Surfaces in general affine space. (English) Zbl 0683.53009

The author studies the geometry of locally strongly convex surfaces M in real affine 3-space with respect to the general affine group A. Under the assumption that the equiaffine mean curvature H is nowhere zero the equiaffine metric G(e) defines a definite pseudo-Riemannian metric \(G:=HG(e)\) which is invariant with respect to A. The author states a Theorema egregium for this metric and gives local and global characterizations of quadrics.
Reviewer: U.Simon

MSC:

53A15 Affine differential geometry
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References:

[1] Affine Differentialgeometrie. Tagungsbericht 48/1986; Math. Forschungsinst. Oberwolfach.
[2] Wendland W. L.: Elliptic systems in the plane. Pitman, 1979. · Zbl 0396.35001
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