Minimal Entropy of Geometric 4-manifolds
نویسنده
چکیده
We show that if M is an oriented closed geometric four manifold the following notions are equivalent, (i) M has zero minimal entropy, h(M) = 0. (ii) M collapses with bounded curvature, VolK(M) = 0. (iii) The simplicial volume of M vanishes, ||M || = 0. (iv) M admits a T -structure. (v) M is modelled on one of the geometries S, CP , S × E, H × E, S̃L2 × E, Nil × E, Nil, Sol 1 , S × E, H × E, Sol m,n, Sol 4 0 , S × S, S × H or E. As a consequence if M is modelled on S × H, H × E, S̃L2 × E, H × E, Sol 1, Sol 4 0 or Sol m,n then the minimal entropy problem cannot be solved for M .
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