arXiv research

The paper defines a new connection on sub-Riemannian manifolds and explores conditions for almost quasi-Sasakian manifolds to be Einstein.

The paper defines Dirac structures on connection spaces and their properties.

Novel ternary structures reveal new interpretations of linear connections.

The paper classifies Lorentzian Lie groups based on Codazzi tensors and quasi-statistical structures.

The paper studies geometric structures in Sol_3 with two connections.

New theory connects geometry without relying on connections.

New connections defined for a specific geometric structure.

New connections found for quaternionic and para-quaternionic structures.

Found a new connected component in symplectic structures.

Combines higher complex structures with flat connections to link to $W$-algebras.

A Lie algebroid classifies G-structures with connections.

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 torsion sharing the geodesics (up to parametrization) with the projective class.…

Sprays on Frechet manifolds connect connections and tangent structures.

A contact projective structure is a contact path geometry the paths of which are among the geodesics of some affine connection. In the manner of T.Y. Thomas there is associated to each contact projective structure an ambient affine connection on a symplectic manifold with one-dimensional fibers over the contact manifol…

Torsion-free connections on $G$-structures are proven for certain groups.

The paper introduces statistical and geometric structures on anti-commutable pre-Leibniz algebroids.

Constructs a connection for Hodge theoretic projective structures on Riemann surfaces.

Relations between conjugate connections with respect to the pair of Norden metrics and to the almost complex structure on almost Norden manifolds are studied. Conjugate connections of the Levi-Civita connections induced by the Norden metrics are obtained. Statistical structures on almost Norden manifolds are considered…

The paper describes projective structures with torsion using formal frames and Thomas-Whitehead connections.

For a system of second order differential equations we determine a nonlinear connection that is compatible with a given generalized Lagrange metric. Using this nonlinear connection, we can find the whole family of metric nonlinear connections that can be associated with a system of SODE and a generalized Lagrange struc…

A hypercomplex structure on a smooth manifold is a triple of integrable almost complex structures satisfying quaternionic relations. The Obata connection is the unique torsion-free connection that preserves each of the complex structures. The holonomy group of the Obata connection is contained in $GL(n, \mathbb{H})$. T…

There has been significant interest in the use of fully-connected graphical models and deep-structured graphical models for the purpose of structured inference. However, fully-connected and deep-structured graphical models have been largely explored independently, leaving the unification of these two concepts ripe for …

The paper studies geometric structures of wormholes using a new connection.

Study of Hermitian and Gauduchon connections on Lie groups with almost Hermitian structures.

In the first part of this series of papers we developed the invariant differentiation with respect to a Cartan connection, we described this procedure in the terms of the underlying principal connections, and we discussed applications of this theory to the construction of natural operators. In this part we will extend …

Exotic hypercomplex structures on a torus are proven to not exist.

Bi-flat F-structures link to differential bicomplexes and Gauss-Manin connections.

Study simplicial volume in fiber bundles with connected groups.

Study on negative Sasakian structures on specific 5-manifolds.

In this paper, we compute canonical connections and Kobayashi-Nomizu connections and their curvature on three-dimensional Lorentzian Lie groups with some product structure. We define algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections. We classify algebraic Ricci solitons assoc…

Higher-order tangent bundles have geometric structures compatible with their iterated bundle structure.

Study integrability of specific geometric structures on odd Courant algebroids.

On a manifold with an almost contact metric structure $(\varphi,\vecξ,η,g,X,D)$ the notions of the interior and the $N$-prolonged connections are introduced. Using the $N$-prolonged connection, a new almost contact metric structure is defined on the distribution $D$. The properties of this structure are studied.

Classifies 3D manifolds with specific structures and automorphisms.

Study on $G_2$-structures manifold geometry.

Rigorous model for 2-gerbes simplifies calculations in physics.

Study jets of flat partial connections in foliations.

Defines non-Abelian gerbes with connections for physical applications.

The study connects conic connections and torsion-free principal connections on G-structures.

Let $F^{2n}=(M,M',F^{\ast})$ be an even-dimensional pseudo-Finsler manifold. We construct an almost hypercomplex structure on any chart domain of a certain atlas of $M'$ by using a considered non-linear connection. Then by using the almost hypercomplex structure we define two new families of Finsler connections. Also w…

The paper explores conditions for manifolds to have specific geometric structures.

In the present work, we introduce a linear connection (preserving the almost product structure and the Riemannian metric) on Riemannian almost product manifolds. This connection, called P-connection, is an analogue of the first canonical connection of Lichnerowicz in the Hermitian geometry and the B-connection in the g…

We construct a connection and a curving on a bundle gerbe associated with lifting a structure group of a principal bundle to a central extension. The construction is based on certain structures on the bundle, i.e. connections and splittings. The Deligne cohomology class of the lifting bundle gerbe with the connection a…

New insights into metrizability of SO(3)-invariant connections, linking Riemann and Finsler structures.

We study the Schouten-van Kampen connection associated to an almost contact or paracontact metric structure. With the help of such a connection, some classes of almost (para) contact metric manifolds are characterized. Certain curvature properties of this connection are found.

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…

Let $G$ be a connected Lie group and $\mathfrak{g}$ its Lie algebra. We denote by $\nabla^0$ the torsion free bi-invariant linear connection on $G$ given by $\nabla^0_XY=\frac12[X,Y],$ for any left invariant vector fields $X,Y$. A Poisson structure on $\mathfrak{g}$ is a commutative and associative product on $\mathfra…

Complete classification of para-Kähler structures on Lie groups.