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Convex affine domains and Markus conjecture. (English) Zbl 1061.52006

The authors investigate convex quasi-homogeneous affine domains with an irreducible projective automorphism group. They show that such a domain is projectively equivalent to a homogeneous affine domain. This result is the cornerstone for some further enquiry on a conjecture by L. Markus (1962): A compact affine manifold \(M\) with parallel volume is complete. Markus’s conjecture is being addressed in the paper, and it is being answered positively for some class of affine manifolds where the projective automorphism group is irreducible.
Reviewer: Johann Lang (Graz)

MSC:

52A99 General convexity
57S25 Groups acting on specific manifolds
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