2 citations · 4 across the 7 of their papers we have counts for
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Collapsing manifolds obtained by Kummer-type constructions
Gabriel P. Paternain, Jimmy Petean
We construct F-structures on a Bott manifold and on some other manifolds obtained by Kummer-type constructions. We also prove that if M=E#X, where E is a fiber bundle with structur…
Zero entropy and bounded topology
Gabriel P. Paternain, Jimmy Petean
We study the existence of Riemannian metrics with zero topological entropy on a closed manifold M with infinite fundamental group. We show that such a metric does not exist if ther…
On the growth rate of contractible closed geodesics on reducible manifolds
Gabriel Paternain, Jimmy Petean
We prove exponential growth rate of contractible closed geodesics for an arbitrary bumpy metric on manifolds of the form X#Y, where the fundamental group of X has a subgroup of fin…
Entropy and collapsing of compact complex surfaces
Gabriel P. Paternain, Jimmy Petean
We study the problem of existence of F-structures on compact complex surfaces, giving a complete classification modulo the gap in the classification of surfaces of class VII. We th…
Minimal entropy and collapsing with curvature bounded from below
Gabriel Paternain, Jimmy Petean
We show that if a closed manifold M admits an F-structure (possibly of rank 0) then its minimal entropy vanishes. In particular, this is the case if M admits a non-trivial circle a…
Einstein manifolds of non-negative sectional curvature and entropy
Gabriel Paternain, Jimmy Petean
We find obstructions to the existence of Einstein metrics of non-negative sectional curvature on a smooth closed simply connected manifold of any dimension. The results are achieve…