19 citations · 45 across the 20 of their papers we have counts for
10 papers · 1 filter
Geography of -manifolds with positive scalar curvature
Agnese Mantione, Rafael Torres
We discuss the geography problem of closed oriented 4-manifolds that admit a Riemannian metric of positive scalar curvature, and use it to survey mathematical work employed to addr…
Existence of Riemannian metrics with positive biorthogonal curvature on simply connected 5-manifolds
Boris Stupovski, Rafael Torres
Using recent work of Bettiol, we show that a first-order conformal deformation of Wilking's metric of almost-positive sectional curvature on yields a family of metr…
An equivalence between pseudo-holomorphic embeddings into almost-complex Euclidean space and CR regular embeddings into complex space
Rafael Torres
We show that a pseudo-holomorphic embedding of an almost-complex -manifold into almost-complex -Euclidean space exists if and only if there is a CR regular embedding…
An orbit space of a nonlinear involution of with nonnegative sectional curvature
Rafael Torres
We describe a construction of Riemannian metrics of nonnegative sectional curvature on a closed smooth nonorientable 4-manifold with fundamental group of order two that realizes a…
Some examples of vanishing Yamabe invariant and minimal volume, and collapsing of inequivalent smoothings and PL-structures
Rafael Torres
In this short note, exploits of constructions of -structures coupled with technology developed by Cheeger-Gromov and Paternain-Petean are seen to yield a procedure to…
A note on collapse, entropy, and vanishing of the Yamabe invariant of symplectic 4-manifolds
Pablo Suárez-Serrato, Rafael Torres
We make use of -structures and technology developed by Paternain - Petean to compute minimal entropy, minimal volume, and Yamabe invariant of symplectic 4-manifolds, a…
On entropies, -structures, and scalar curvature of certain involutions
Rafael Torres
In this short note, we analyze geometric properties of orbit spaces of certain involutions in dimensions four, five, and six. We consider constructions of -structures…
On the number of type change loci of a generalized complex structure
Rafael Torres, Jonathan Yazinski
In this note, we describe a procedure to construct generalized complex structures with an arbitrarily large number of type change loci on products of the circle with a connected su…
Constructions of generalized complex structures in dimension four
Rafael Torres
Four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have…
On Einstein metrics, normalized Ricci flow and smooth structures on $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$
Rafael Torres
In this paper, first we consider the existence and non-existence of Einstein metrics on the topological 4-manifolds $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$ (for $k \in {11, 13, 14…