arXiv research

The study lifts certain Sasakian manifolds to quasi-Einstein spacetimes.

We consider axisymmetric stationary dirty black holes with regular non-extremal or extremal horizons, and compute their on-horizon Petrov types. The Petrov type (PT) in the frame of the observer crossing the horizon can be different from that formally obtained in the usual (but singular in the horizon limit) frame of a…

The paper classifies Weyl tensors in Riemannian 4-manifolds via Lorentzian deformation.

On an oriented 4-manifold, we examine the geometry that arises when the curvature operator of a Riemannian or Lorentzian metric $g$ commutes, not with its own Hodge star operator, but rather with that of another semi-Riemannian metric $h$ that is a suitable deformation of $g$. We classify the case when one of these met…

Study properties of null string congruences in complex and real pseudo-Riemannian spaces.

Study para-Kähler-Einstein metrics and their non-integrable twistor distributions.

The paper classifies and explores isoparametric hypersurfaces in pseudo-Riemannian space forms.

Derives new symmetry operators for linearized gravity.

The local structure of the manifolds named in the title is described. Although curvature homogeneous, they are not, in general, locally homogeneous. Not all of them are Ricci-flat, which answers an existence question about type III Jordan-Osserman metrics, raised by Diaz-Ramos, Garcia-Rio and Vazquez-Lorenzo (2006).

The Einstein Equation on 4-dimensional Lorentzian manifolds admitting recurrent null vector fields is discussed. Several examples of a special form are constructed. The holonomy algebras, Petrov types and the Lie algebras of Killing vector fields of the obtained metrics are found.

Optical (or Robinson) structures are one generalisation of four-dimensional shearfree congruences of null geodesics to higher dimensions. They are Lorentzian analogues of complex and CR structures. In this context, we extend the Goldberg-Sachs theorem to five dimensions. To be precise, we find a new algebraic condition…

2D twistor manifolds explain Teukolsky equations for rotating black holes.

Kähler metrics derived from Lorentzian geometry in 4D.

Study on mode stability of gravitational instantons of type D.

The paper constructs a new Ricci-flat metric on almost abelian Lie groups.

We study the geometric properties of holomorphic distributions of totally null $m$-planes on a $(2m+ε)$-dimensional complex Riemannian manifold $(\mathcal{M}, \bm{g})$, where $ε\in {0,1}$ and $m \geq 2$. In particular, given such a distribution $\mathcal{N}$, say, we obtain algebraic conditions on the Weyl tensor and t…

The study characterizes and classifies specific types of manifolds using conformal and quasi-Einstein properties.

It is well known that the classification of the Weyl tensor in Lorentzian manifolds of dimension four, the so called Petrov classification, was a great tool to the development of general relativity. Using the bivector approach it is shown in this article a classification for the Weyl tensor in all four-dimensional mani…

In this paper we consider the field equations for linearized gravity and other integer spin fields on the Kerr spacetime, and more generally on spacetimes of Petrov type D. We give a derivation, using the GHP formalism, of decoupled field equations for the linearized Weyl scalars for all spin weights and identify the g…

Algorithm classifies five-dimensional spacetimes, generalizing Karlhede's for four dimensions.

Conformally quasi-recurrent (CQR)_n pseudo-Riemannian manifolds are investigated, and several new results are obtained. It is shown that the Ricci tensor and the gradient of the fundamental vector are Weyl compatible tensors (the notion was introduced recently by the authors and applies to significative space-times), (…

The Petrov classification is an important algebraic classification for the Weyl tensor valid in 4-dimensional space-times. In this thesis such classification is generalized to manifolds of arbitrary dimension and signature. This is accomplished by interpreting the Weyl tensor as a linear operator on the bundle of p-for…

We consider static spacetimes whose spatial part admits foliations with the extrinsic curvature tensor K_{ab}=0. There are two complementary cases when the gradient of the lapse function points 1) to the direction of foliation or 2) orthogonally to it. Case 1) gives generalization of metrics like Bertotti-Robinson or N…

The most recent update of financial option models is American options under stochastic volatility models with jumps in returns (SVJ) and stochastic volatility models with jumps in returns and volatility (SVCJ). To evaluate these options, mesh-based methods are applied in a number of papers but it is well-known that the…

We consider Legendrian contact structures on odd-dimensional complex analytic manifolds. We are particularly interested in integrable structures, which can be encoded by compatible complete systems of second order PDEs on a scalar function of many independent variables and considered up to point transformations. Using …

The study finds obstructions for certain Weyl curvature tensors on manifolds.

It is shown that a self-dual neutral Einstein four-manifold of Petrov type III, admitting a two-dimensional null parallel distribution compatible with the orientation, cannot be compact or locally homogeneous, and its maximum possible degree of mobility is 3. Diaz-Ramos, Garcia-Rio and Vazquez-Lorenzo found a general c…

In this paper we derive a differential identity for linearized gravity on the Kerr spacetime and more generally on vacuum spacetimes of Petrov type D. We show that a linear combination of second derivatives of the linearized Weyl tensor can be formed into a complex symmetric 2-tensor $\mathcal{M}_{ab}$ which solves the…

The study characterizes spacetimes with quasi-constant sectional curvature and explores their properties in $\mathcal{F}(\mathcal{R})$-gravity.

An almost Robinson structure on an $n$-dimensional Lorentzian manifold $(\mcM,g)$, where $n=2m+ε$, $ε\in \{ 0 ,1 \}$, is a complex $m$-plane distribution $\mcN$ that is totally null with respect to the complexified metric, and intersects its complex conjugate in a real null line distribution $\mcK$, say. When $\mcN$ an…

The Teukolsky connection is linked to a complex structure on Einstein spacetimes.

Let $C(2n, 3)$ be the family of two bridge knots of slope $(4n+1)/(6n+1)$. We calculate the volumes of the $C(2n, 3)$ cone-manifolds using the Schläfli formula. We present the concrete and explicit formula of them. We apply the general instructions of Hilden, Lozano, and Montesinos-Amilibia and extend the Ham, Mednykh,…

Researchers correct earlier work on surgeries of Gieseking's hyperbolic simplex manifold.

Wilson lines in gauge theories admit several path integral descriptions. The first one (due to Alekseev-Faddeev-Shatashvili) uses path integrals over coadjoint orbits. The second one (due to Diakonov-Petrov) replaces a 1-dimensional path integral with a 2-dimensional topological $σ$-model. We show that this $σ$-model i…

In this paper the Weyl tensor is used to define operators that act on the space of forms. These operators are shown to have interesting properties and are used to classify the Weyl tensor, the well known Petrov classification emerging as a special case. Particularly, in the Euclidean signature this classification turns…

The study characterizes spacetime and modified gravity models using projective curvature tensor.

Develops VPINNs for solving PDEs with reduced training cost and improved accuracy.

GPS model predicts subspace-valued functions efficiently.

This paper simplifies hedge ratios in financial models using pathwise algorithmic differentiation.

Typilus predicts types for Python programs using neural networks.

LambdaNet infers TypeScript types using graph neural networks.

Study shows partially-typed NER datasets can match fully-typed ones in model performance.

New model predicts fine-grained types for high-multiplicity entities.

The generic fiber of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is an abelian variety. Associate a polarization type to such Lagrangian fibrations coming from polarizations on a generic fiber. We prove that this polarization type is constant in families of Lagrangian fibrations. Further, w…

Paper introduces a new adversarial attack type that cheats classifiers with significant changes.

We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a …

Constructs odd Khovanov homotopy types for links, linking them to even types.

Study shows infinite real homotopy types for complex nilmanifolds.