Affine spheres with prescribed Blaschke metric
Keyword(s):
It is proved that the equality ?ln |k-?| = 6k, where k is the Gaussian curvature of a metric tensor 1 on a 2-dimensional manifold is a sufficient and necessary condition for local realizability of the metric as the Blaschke metric of some affine sphere. Consequently, the set of all improper local affine spheres with nowhere-vanishing Pick invariant can be parametrized by harmonic functions.
2018 ◽
Vol 16
(06)
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pp. 1850053
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2017 ◽
Vol 13
(8)
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pp. 155014771772629
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2013 ◽
Vol 278-280
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pp. 1687-1691