Weierstraß-type representation of affine spheres. (English) Zbl 1031.53021
In this paper the authors study the problem of explicit construction of affine spheres and develop (in detail) an approach based on a combination of analytic and algebraic techniques. In particular, it is shown that to construct an affine sphere one needs to solve two special ordinary differential equations and then study the splitting of an associated loop group of which the moving frame of the affine sphere is a member. They illustrate their approach by constructing examples which include general ruled surfaces.
Reviewer: V.I.Oliker (Atlanta)
MSC:
| 53A15 | Affine differential geometry |
References:
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