Related papers: Second-order PDEs in 3D with Einstein-Weyl conform…

We investigate complex quaternion-valued exterior differential forms over 4-dimensional Lorentzian spacetimes and explore Weyl spinor fields as minimal left ideals within the complex quaternion algebra. The variational derivation of the…

We show how to lift a generic non-scale invariant action in Einstein frame into a locally conformally-invariant (or Weyl-invariant) theory and present a new general form for Lagrangians consistent with Weyl symmetry. Advantages of such a…

In this work we predict a family of noncentrosymmetric two-dimensional (2D) Weyl semimetals composed by porous Ge and SiGe structures. These systems are energetically stable graphenylene-like structures with a buckling, spontaneously…

We present a model of electroweak symmetry breaking in a warped extra dimension where electroweak symmetry is broken at the UV (or Planck) scale. An underlying conformal symmetry is broken at the IR (or TeV) scale generating masses for the…

We show that a properly convex projective structure $\mathfrak{p}$ on a closed oriented surface of negative Euler characteristic arises from a Weyl connection if and only if $\mathfrak{p}$ is hyperbolic. We phrase the problem as a…

Basic quantities related to 2-D gravity, such as Polyakov extrinsic action, Nambu-Goto action, geometrical action, and Euler characteristic are studied using generalized Weierstrass-Enneper (GWE) inducing of surfaces. Connection of the GWE…

A special class of (complex) para-Hermite Einstein spaces is analyzed. For this class of spaces the self-dual Weyl tensor is type-[D] in the Petrov-Penrose classification. The anti-self-dual Weyl tensor is algebraically degenerate,…

A comparison is given between the Newtonian and Einsteinian frames of gravitation. From this it is shown that there exist a weak connection to gravitation and electromagnetism. This connection is then studied more thoroughly with the Weyl…

We obtain a full characterization of Einstein-Maxwell $p$-form solutions $(\boldsymbol{g},\boldsymbol{F})$ in $D$-dimensions for which all higher-order corrections vanish identically. These thus simultaneously solve a large class of…

The second H. Weyl curvature invariant of a Riemannian manifold, denoted $h_4$, is the second curvature invariant which appears in the well known tube formula of H. Weyl. It coincides with the Gauss-Bonnet integrand in dimension 4. A…

Weyl conformal geometry may play a role in early cosmology where effective theory at short distances becomes conformal. Weyl conformal geometry also has a built-in geometric Stueckelberg mechanism: it is broken spontaneously to Riemannian…

We study whether the relations between the Weyl anomaly, entanglement entropy (EE), and thermal entropy of a two-dimensional (2D) conformal field theory (CFT) extend to 2D boundaries of 3D CFTs, or 2D defects of $D \geq 3$ CFTs. The Weyl…

We consider $d$-dimensional solutions to the electrovacuum Einstein-Maxwell equations with the Weyl tensor of type N and a null Maxwell $(p+1)$-form field. We prove that such spacetimes are necessarily aligned, i.e. the Weyl tensor of the…

We classify integrable Hamiltonian equations in 3D with the Hamiltonian operator d/dx, where the Hamiltonian density h(u, w) is a function of two variables: dependent variable u and the non-locality w such that w_x=u_y. Based on the method…

We develop a procedure to implement the method of quadric ansatz to a class of second order partial differential equations (PDEs), which includes the four-dimensional K\"ahler-Einstein equation with symmetry and the one-sided type-D…

Any oriented $4$-dimensional Einstein metric with semi-definite sectional curvature satisfies the pointwise inequality \[ \frac{|s|}{\sqrt{6}}\geq|W^+|+|W^-|, \] where $s$, $W^+$ and $W^-$ are respectively the scalar curvature, the…

We look for four dimensional Einstein-Weyl spaces equipped with a regular Bianchi metric. Using the explicit 4-parameters expression of the distance obtained in a previous work for non-conformally-Einstein Einstein-Weyl structures, we show…

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…

In the standard Einstein's theory the exterior gravitational field of any static and axially symmetric stellar object can be described by means of a single function from which we obtain a metric into a four-dimensional space-time. In this…

We study the algebra of functions on the Iwahori group via the category of graded bounded representations of its Lie algebra. In particular, we identify the standard and costandard objects in this category with certain generalized Weyl…