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- W2949242008 abstract "The expression (-1/u) times the Hessian of u transforms as a symmetric (0,2) tensor under projective coordinate transformations, so long as u transforms as a section of a certain line bundle. On a locally projectively flat manifold M, the section u can be regarded as a metric potential analogous to the local potential in Kahler geometry. If M is compact and u is a negative section of the dual of the tautological bundle whose Hessian is positive definite, then M is projectively equivalent to a quotient of a bounded convex domain in R^n. The same is true if M has a boundary on which u=0. This theorem is analogous to a result of Schoen and Yau in locally conformally flat geometry. The proof uses affine differential geometry techniques developed by Cheng and Yau." @default.
- W2949242008 created "2019-06-27" @default.
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- W2949242008 date "2001-08-30" @default.
- W2949242008 modified "2023-09-27" @default.
- W2949242008 title "Riemannian Metrics on Locally Projectively Flat Manifolds" @default.
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