Related papers: Regular ambitoric $4$-manifolds: from Riemannian K…

We prove that a compact quaternionic-K\"{a}hler manifold of dimension $4n\geq 8$ admitting a conformal-Killing 2-form which is not Killing, is isomorphic to the quaternionic projective space, with its standard quaternionic-K\"{a}hler…

We consider rotating black hole configurations of self-gravitating maps from spacetime into arbitrary Riemannian manifolds. We first establish the integrability conditions for the Killing fields generating the stationary and the…

We present a local classification of conformally equivalent but oppositely oriented 4-dimensional Kaehler metrics which are toric with respect to a common 2-torus action. In the generic case, these "ambitoric" structures have an intriguing…

We obtain topological obstructions to the existence of a complete Riemannian metric with uniformly positive scalar curvature on certain (non-compact) $4$-manifolds. In particular, such a metric on the interior of a compact contractible…

R Kerr's Ricci-flat Lorentz 4-manifold was shown by B Carter in 1968 to support a classically completely integrable system of geodesics; here we interpret this system in terms of a locally conformally symplectic structure, which we identify…

We give an explicit local classification of conformally equivalent but oppositely oriented Kaehler metrics on a 4-manifold which are toric with respect to a common 2-torus action. In the generic case, these structures have an intriguing…

A Riemannian manifold is called geometrically formal if the wedge product of any two harmonic forms is again harmonic. We classify geometrically formal compact 4-manifolds with nonnegative sectional curvature. If the sectional curvature is…

We consider the metric of a generic axially symmetric rotating stationary black hole. The general approach is developed that enables us to construct coordinate frame regular near the horizon. As explicit examples, the Kerr and…

Conformal Killing forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We show the existence of…

An extremal rotating black hole in arbitrary dimension, along with time translations and rotations, possesses a number of hidden symmetries characterized by the second rank Killing tensors. As is known, in the near horizon limit the…

We study 4-dimensional simply connected Lie groups $G$ with left-invariant Riemannian metric $g$ admitting non-trivial conformal Killing 2-forms. We show that either the real line defined by such a form is invariant under the group action,…

We give a classification for connected complete locally irreducible Riemannian manifolds with nonpositive curvature operator, which admit a nonzero closed or co-closed conformal Killing $L^{2}-$form. Moreover, we prove vanishing theorems…

We classify, up to homeomorphisms, the closed simply-connected 4-manifolds that admit a Riemannian metric for which averages of pairs of sectional curvatures of orthogonal planes are positive.

A local classification of locally conformal flat Riemannian Einstein-like four-manifolds as well as a local classification of all locally conformal flat Riemannian four-manifolds for which all Jacobi operators have parallel eigenspaces…

We prove that if a compact Riemannian 4-manifold with positive sectional curvature satisfies a Kato type inequality, then it is definite. We also discuss some new insights for compact Riemannian 4-manifolds of positive sectional curvature.

We obtain a coordinate independent algorithm to determine the class of conformal Killing vectors of a locally conformally flat $n$-metric $\gamma$ of signature $(r,s)$ modulo conformal transformations of $\gamma$. This is done in terms of…

We completely determine, up to homeomorphism, which simply connected compact oriented 4-manifolds admit scalar-flat, anti-self-dual Riemannian metrics. The key new ingredient is a proof that the connected sum of five reverse-oriented…

In this note we prove that a four-dimensional compact oriented half-confor\-mally flat Riemannian manifold $M^4$ is topologically $\mathbb{S}^{4}$ or $\mathbb{C}\mathbb{P}^{2},$ provided that the sectional curvatures all lie in the interval…

Hermitian non-K\"ahler Einstein 4-manifolds have a quasi-locally conserved charge associated to spin-lowering via Killing spinors, and corresponding to a parameter of the moduli space. This charge is evaluated for all explicitly known…

In this paper we describe the topology of 4-dimensional closed orientable Riemannian manifolds with a uniform lower bound of sectional curvature and with a uniform upper bound of diameter which collapse to metric spaces of lower dimensions.…