Related papers: Strongly positive curvature
We examine a condition on a simply connected 2-complex X ensuring that groups acting properly on X are coherent. This extends earlier work on 2-complexes with negative sectional curvature which covers the case that G acts freely. Our…
A central theme in Riemannian geometry is understanding the relationships between the curvature and the topology of a Riemannian manifold. Positive isotropic curvature (PIC) is a natural and much studied curvature condition which includes…
Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though,…
We show that the sectional curvature of a Riemannian manifold is nonnegative if, and only if, the entropy functional is matrix displacement convex. As an application we obtain intrinsic dimensional evolution variational inequalities, and…
We present a necessary and sufficient condition for the strict positive definiteness of a real, continuous, isotropic and positive definite kernel on a two-point compact homogeneous space. The characterization adds to others previously…
We show that a shrinking Ricci soliton with positive sectional curvature must be compact. This extends a result of Perelman in dimension three and improves a result of Naber in dimension four, respectively.
Let $E \subset \mathbb R^d$, $d \ge 2$, be compact, and let $\phi(x,y)$ be a smooth function satisfying the Phong--Stein rotational curvature condition on $\{\phi(x,y)=1\}$. We prove that if $\dim_{\mathcal H}(E)>1$, then $$…
We obtain a class of locally symmetric Kaehler Einstein structures on the cotangent bundle of a Riemannian manifold of negative sectional curvature. Similar results are obtained in the case of a Riemannian manifold of positive sectional…
We introduce the notion of positivity for a real basic $(1,1)$ class in basic Bott-Chern cohomology group on foliated manifolds, and study the relationship between this positivity and the negativity of transverse holomorphic sectional…
The projective curvature tensor $P$ is invariant under a geodesic preserving transformation on a semi-Riemannian manifold. It is well known that $P$ is not a generalized curvature tensor and hence it possesses different geometric properties…
We consider the blowup of a point of a compact K\"ahler manifold and a metric of the form $\mu^*h + t b$ on it, where $h$ is a K\"ahler metric on the original manifold and $b$ is Hermitian form that looks like the Fubini--Study metric near…
One of the main methods of constructing new spaces with positive or almost positive curvature is the study of biquotients first studied in detail by Eschenburg. We classify orbifold biquotients of the Lie Group $SU(3)$, and construct a new…
We study classical structures in various categories of completely positive morphisms: on sets and relations, on cobordisms, on a free dagger compact category, and on Hilbert spaces. As an application, we prove that quantum maps with…
Conjecture 1 of Stanley Chang: "Positive scalar curvature of totally nonspin manifolds" asserts that a closed smooth manifold M with non-spin universal covering admits a metric of positive scalar curvature if and only if a certain…
In the context of mathematical cosmology, the study of necessary and sufficient conditions for a semi-Riemannian manifold to be a (generalised) Robertson-Walker space-time is important. In particular, it is a requirement for the development…
We study the positive Hermitian curvature flow on the space of left-invariant metrics on complex Lie groups. We show that in the nilpotent case, the flow exists for all positive times and subconverges in the Cheeger-Gromov sense to a…
In this paper we present a rigidity theorem for locally isometric hypersurfaces with a curvature restriction in de Sitter space. This is an analogue to the case for Riemannian space forms given by Guan and Shen in [5].
We give a new proof for the local existence of a smooth isometric embedding of a smooth $3$-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into $6$-dimensional Euclidean space. Our proof avoids the sophisticated…
We study the curvature of a manifold on which there can be defined a complex-valued submersive harmonic morphism with either, totally geodesic fibers or that is holomorphic with respect to a complex structure which is compatible with the…
We extend a positive Ricci curvature gluing theorem of Perelman to a range of positive intermediate curvature conditions, ranging from positive scalar curvature up to (and including) positive sectional curvature. As an application of this,…