arXiv research

Holomorphic structures on Oeljeklaus-Toma manifolds are shown to be locally homogeneous.

Defines structure constants for specific geometric structures on Lie groups.

Proves local solvability for $G_2$-structures with Poisson equations.

We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct locally conformally symplectic structures on compact quotients of all four-dimensional connected and simply connected solvable Lie groups.

Motivated by analogous results in locally conformal symplectic geometry, we study different classes of G$_2$-structures defined by a locally conformal closed 3-form. In particular, we give a complete characterization of invariant exact locally conformal closed G$_2$-structures on simply connected Lie groups, and we pre…

Localized diffusion models reduce training complexity by exploiting low-dimensional structure.

Study on median algebra structures on Euclidean spaces and manifolds with local CAT(0) cubulation.

This article investigates a few questions about orbits of local automorphisms in manifolds endowed with rigid geometric structures. We give sufficient conditions for local homogeneity in a broad class of such structures, namely Cartan geometries, extending a classical result of Singer about locally homogeneous Riemanni…

We prove that under some purely algebraic conditions every locally homogeneous structure modelled on some homogeneous space is induced by a locally homogeneous structure modelled on a different homogeneous space.

In this article, we discuss which semisimple locally symmetric spaces admit an AHS--structure invariant to local symmetries. We classify them for all types of AHS--structures and determine possible equivalence classes of such AHS--structures.

Local formulas for Poisson structures on wrinkled fibrations are derived.

LASE improves local network structure visualization by targeting locally low-dimensional regions.

Classifies complex Dirac structures with invariants and local structure.

New method controls error in low-dimensional marginals of spatial models.

Extends Gromov non-squeezing to locally conformally symplectic structures.

We present some examples of locally conformal symplectic structures of the first kind on compact nilmanifolds which do not admit Vaisman metrics. One of these examples does not admit locally conformal Kähler metrics and all the structures come from left-invariant locally conformal symplectic structures on the correspon…

Study local structure of Einstein metrics with boundary conditions.

Estimates manifold dimension using local graph structure.

Unified framework for Arnold-type invariants via dual complexes and finite-difference structures.

This work investigates how GCNs should handle local structure discrepancies in testing nodes.

Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries. In fact, under regularity assumptions, any given ODE always admits solvable struc…

Local tri-Hamiltonian structure for Ablowitz-Ladik hierarchy established.

A Hermitian structure on a manifold is called locally conformally Kähler (LCK) if it locally admits a conformal change which is Kähler. In this survey we review recent results of invariant LCK structures on solvmanifolds and present original results regarding the canonical bundle of solvmanifolds equipped with a Vaisma…

We give a notion of compatibility between a Riemannian structure and a Jacobi structure. We prove that in case of fundamental examples of Jacobi structures : Poisson structures, contact structures and locally conformally symplectic structures, we get respectively Riemann-Poisson structures in the sense of M. Boucetta, …

In this paper we examine a novel addition to the known methods for learning Bayesian networks from data that improves the quality of the learned networks. Our approach explicitly represents and learns the local structure in the conditional probability tables (CPTs), that quantify these networks. This increases the spac…

Study local properties of homogeneous ANR-spaces, proving dimension full-valuedness.

Local normal forms for symmetrical contact structures on 3-manifolds.

We solve the local equivalence problem for sub-Riemannian structures on (2n + 1)-dimensional manifolds. We show that two sub-Riemannian structures are locally equivalent if and only if? their corresponding canonical linear connections are equivalent. When n = 1, these connections coincide with the generalized Tanaka-We…

We give a notion of compatibility between a Riemannian metric and a Jacobi structure. We prove that in case of Poisson structures, contact structures and locally conformally symplectic structures, fundamental examples of Jacobi structures, we get respectively Riemann-Poisson structures in the sense of M. Boucetta, $\fr…

The paper localizes an index and provides a condition for the orientability of a monopole moduli space.

This work extends locally conformal analysis to multi-Hamiltonian settings, providing new geometric structures and Hamiltonian dynamics.

b-LOAD extends local causal discovery with prior knowledge, improving causal effect estimation.

Study of recurrent Lorentzian Weyl spaces with detailed local and global structures.

Study local structure of knot group representations into SL(n,C).

In this paper a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group $\mathbb H_3$, or its conformal classification coincides with the metric one…

We study the Laplacian flow of a $\mathrm{G}_2$-structure where this latter structure is claimed to be Locally Conformal Parallel. The first examples of long time solutions of this flow with the Locally Conformal Parallel condition are given. All of the solutions are ancient and Laplacian soliton of shrinking type. The…

Investigate local Lie group structure of bisections over compact manifolds

Study non-Kähler metrics on complex nilmanifolds, proving torus structure under certain conditions.

The paper develops quaternionic toric geometry and classifies local actions.

We study holomorphic locally homogeneous geometric structures modelled on line bundles over the projective line. We classify these structures on primary Hopf surfaces. We write out the developing map and holonomy morphism of each of these structures explicitly on each primary Hopf surface.

For any locally defined $G_{2}-$structure and Hermitian-Yang-Mills connection on $S^{6}$, the $G_{2}-$monopole equation always admits a local solution that is asymptotic to the HYM-connection.

Construct quaternionic-Kähler metrics from special Kähler manifolds with specific BPS structure variations.

We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Cartan geometries and their explicit description. This allows us to describe the structure of symmetric geometric structur…

Learning a Bayesian network structure from data is an NP-hard problem and thus exact algorithms are feasible only for small data sets. Therefore, network structures for larger networks are usually learned with various heuristics. Another approach to scaling up the structure learning is local learning. In local learning…

Necessary and sufficient conditions for the existence of a hyper-parahermitian connection with totally skew-symmetric torsion (HPKT-structure) are presented. It is shown that any HPKT-structure is locally generated by a real (potential) function. An invariant first order differential operator is defined on any almost h…

In this work, we present an application of Locally Interpretable Machine-Agnostic Explanations to 2-D chemical structures. Using this framework we are able to provide a structural interpretation for an existing black-box model for classifying biologically produced fuel compounds with regard to Research Octane Number. T…

We study locally homogeneous rigid geometric structures on surfaces. We show that a locally homogeneous projective connection on a compact surface is flat. We also show that a locally homogeneous unimodular affine connection on a two dimensional torus is complete and, up to a finite cover, homogeneous. Let $\nabla$ be …

Study local geometry of bi-contact structures on 3-manifolds.