We provide several results on the existence of metrics non-negative sectional curvature vector bundles over certain cohomogeneity one manifolds and homogeneous spaces up to suitable stabilization. Beside explicit constructions metrics, this is achieved by identifying equivariant structures upon these via a comparison their non-equivariant K-theory. For this, in particular, we transcribe K-theor...

We construct the normal forms of null-K\"ahler metrics: pseudo-Riemannian metrics admitting a compatible parallel nilpotent endomorphism tangent bundle. Such are examples non-Riemannian holonomy reduction, and (in complexified setting) appear in Bridgeland stability conditions moduli spaces Calabi-Yau three-folds. Using twistor methods we show that, dimension four - where there is connection wi...

In this paper, we consider a closed Riemannian manifold $$M^{n+1}$$ with dimension $$3\le n+1\le 7$$ , and compact Lie group G acting as isometries on M cohomogeneity at least 3. Suppose the union of non-principal orbits $$M{\setminus } M^{reg}$$ is smooth embedded submanifold most $$n-2$$ . Then for any $$c\in \mathbb {R}$$ show existence nontrivial, smooth, closed, almost embedded, G-invarian...

One of the classical problems in differential geometry is the investigation of closed manifolds which admit Riemannian metrics with given lower bounds for the sectional or the Ricci curvature and the study of relations between the existence of such metrics and the topology and geometry of the underlying manifold. Despite many efforts during the past decades, this problem is still far from being...

We find complete expanding Kähler-Ricci solitons of two types. The first are cohomogeneity one under the action (2m - 1)-dimensional Heisenberg group or a certain quotient it, for any m ? 2. second type, which generalizes first, reside on ?*-bundles over compact Kähler Ricci-flat manifolds, admit an S1 by isometries, and have ends. Both types local structure stemming from ansatz described in [2...