相关论文: On the Weyl tensor of a self-dual complex 4-manifo…

Seiberg-Witten theory leads to a delicate interplay between Riemannian geometry and smooth topology in dimension four. In particular, the scalar curvature of any metric must satisfy certain non-trivial estimates if the manifold in question…

We realize every closed flat 3-manifold as a cusp section of a complete, finite-volume hyperbolic 4-manifold whose symmetry group acts transitively on the set of cusps. Moreover, for every such 3-manifold, a dense subset of its flat metrics…

If a smooth compact 4-manifold M admits a Kaehler-Einstein metric g of positive scalar curvature, Gursky showed that its conformal class [g] is an absolute minimizer of the Weyl functional among all conformal classes with positive Yamabe…

We consider weighted parallel spinors in Lorentzian Weyl geometry in arbitrary dimensions, choosing the weight such that the integrability condition for the existence of such a spinor, implies the geometry to be Einstein-Weyl. We then use…

Ehlers, Pirani, and Schild argued that measurements of null and timelike geodesics yield Weyl and projective connections, respectively, with compatibility in the lightlike limit giving an integrable Weyl connection. Their conclusions hold…

We find geometric conditions on a Hermitian-Weyl manifold under which the complex structure is a pseudo-harmonic map in the sense of G. Kokarev \cite{K09} from the manifold into its twistor space. This is done under the assumption that the…

A referee found an error in the proof of the Theorem 2 that we could not fix. More precisely, the proof of Lemma 2.1 is incorrect. Hence the fact that integer cohomology of complement of toric Weyl arrangements is torsion free is still a…

Weyl geometry is a natural extension of conformal geometry with Weyl covariance mediated by a Weyl connection. We generalize the Fefferman-Graham (FG) ambient construction for conformal manifolds to a corresponding construction for Weyl…

Consistency of Weyl natural gauge, Lorentz gauge and nonlinear gauge is studied in Weyl geometry. Field equations in generalized Weyl-Dirac theory show that spinless electron and photon are topological defects. Statistical metric and…

In this paper we consider an Einstein-type equation which generalizes important geometric equations, like static and critical point equations. We prove that a complete Einstein-type manifold with fourth-order divergence-free Weyl tensor and…

We prove that, in a space-time of dimension n>3 with a velocity field that is shear-free, vorticity-free and acceleration-free, the covariant divergence of the Weyl tensor is zero if the contraction of the Weyl tensor with the velocity is…

We introduce and study the notion of null manifold. This is a smooth manifold ${\mathcal N}$ endowed with a degenerate metric $\gamma$ with one-dimensional radical at every point. We also define the notion of ruled null manifold, which is a…

We analyze gravitational theories with quadratic curvature terms, including the case of conformally invariant Weyl gravity, motivated by the intention to find a renormalizable theory of gravity in the ultraviolet region, yet yielding…

We show that a class of solutions of minimal supergravity in five dimensions is given by lifts of three--dimensional Einstein--Weyl structures of hyper-CR type. We characterise this class as most general near--horizon limits of…

Unconventional Weyl semimetals have attracted intensive research interest in condensed matter physics and materials science, but they are very rare in two dimensions. In this work, based on symmetry analysis and the first-principles…

The space of tensors of metric curvature type on a Euclidean vector space carries a two-parameter family of orthogonally invariant commutative nonassociative multiplications invariant with respect to the symmetric bilinear form determined…

We study various mathematical aspects of the charged rotating black hole with two equal-magnitude angular momenta in five dimensions. We introduce a coordinate system that is regular on the horizon and in which Einstein-Maxwell equations…

Einstein-Weyl geometry is a triple (D,g,w), where D is a symmetric connection, [g] is a conformal structure and w is a covector such that: (i) connection D preserves the conformal class [g], that is, Dg=wg; (ii) trace-free part of the…

Starting from a real analytic surface $\mathcal{M}$ with a real analytic conformal Cartan connection A. Bor\'owka constructed a minitwistor space of an asymptotically hyperbolic Einstein-Weyl manifold with $\mathcal{M}$ being the boundary.…

We study the relations between the projective and the almost conformally symplectic structures on a smooth even dimensional manifold. We describe these relations by a single almost conformally symplectic connection with totally trace--free…