arXiv research

Formulae for non-symmetric connections derived from covariant derivatives.

New invariants found for mappings between non-symmetric affine spaces.

It is developed the considerations from (S. M. Minčić, [14, 15]) about curvature tensors and pseudotensors for a non-symmetric affine connection space in this paper. How many kinds of covariant derivatives are enough to be defined for complete researching in the field of non-symmetric affine connection spaces is examin…

We consider equitorsion second type almost geodesic mappings of a non-symmetric affine connection space in this article. Using different computational methods, we obtained some invariants of these mappings. Last generalized Thomas projective parameter and Weyl projective tensor as invariants of a second type almost geo…

This paper is devoted to a systematic study and classification of invariant affine or metric connections on certain classes of naturally reductive spaces. For any non-symmetric, effective, strongly isotropy irreducible homogeneous Riemannian manifold $(M=G/K, g)$, we compute the dimensions of the spaces of $G$-invarian…

New connections defined for a specific geometric structure.

There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the contact distribution and an almost contact B-metric structure generated by the pair of associated B-metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the basic clas…

Paper generalizes connections between Lie groups and affine connections.

Study non-symmetric non-metric connections on Kenmotsu manifolds.

Einstein's non-symmetric geometry uses Bochner's technique to prove decomposition and vanishing results.

Newton's method tackles nonlinear mappings into vector bundles with connections and retractions.

Method extends eigenfunction construction to non-symmetric spaces.

We reconcile between two classical models of edge-dislocations in solids. The first model, dating from the early 1900s models isolated edge-dislocations as line singularities in locally-Euclidean manifolds. The second model, dating from the 1950s, models continuously-distributed edge-dislocations as smooth manifolds en…

Connections with (skew-symmetric) torsion on non-symmetric Riemannian manifold satisfying the Einstein metricity condition (NGT with torsion) are considered. It is shown that an almost Hermitian manifold is an NGT with torsion if and only if it is a Nearly Kähler manifold. In the case of an almost contact metric manifo…

It is well-known that sigma-models with symmetric target spaces are classically integrable. At the example of the model with target space the flag manifold U(3)/U(1)^3 -- a non-symmetric space -- we show that the introduction of torsion allows to cast the equations of motion in the form of a zero-curvature condition fo…

We generalize reduction theorems for classical connections to operators with values in $k$-th order natural bundles. Using the first reduction theorem in order two we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.

New estimates show all stable Einstein manifolds are linear stable with respect to Perelman's ν-entropy.

Study shows non-symmetric convex sets have full boundary limits.

New stable metric found on a complex space.

Study new symmetries in non-symmetric spaces and discontinuous groups.

In this paper, we studied the full Einstein-Hilbert actions with respect to non-symmetric metrics and the corresponding torsion. The first concrete result in this paper are the general formulae for pressure and density with respect to the Madsen's article (the equation (3.1), in [10]). Based on these results, we obtain…

This paper is a review of the twistor theory of irreducible G-structures and affine connections. Long ago, Berger presented a very restricted list of possible irreducibly acting holonomies of torsion-free affine connections. His list was complete in the part of metric connections, while the situation with holonomies of…

Study special affine connections on symmetric spaces and their products.

The paper develops methods to generate invariant quantities in Metric-Affine Geometry.

We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine connections.

This paper deals with affine connections on real manifolds. We give a new characterization of flat affine connections on real manifolds by means of certain affine representations of the Lie group of automorphisms preserving the connection. Then we specialize the characterization to the case of a left invariant connecti…

Calculates affine transformations for specific homogeneous spaces.

Paper finds conditions for different norms to produce same billiard paths.

In recent years, a close connection between supergravity, string effective actions and generalized geometry has been discovered that typically involves a doubling of geometric structures. We investigate this relation from the point of view of graded geometry, introducing an approach based on deformations of graded Pois…

Study on completeness in affine and statistical geometry.

We show that a connection with skew-symmetric torsion satisfying the Einstein metricity condition exists on an almost contact metric manifold exactly when it is D-homothetic to a cosymplectic manifold. In dimension five, we get that the existence of a connection with skew torsion satisfying the Einstein metricity condi…

Affine connections linked to Riccati distributions on compact surfaces.

We study the existence of a natural `linearisation' process for generalised connections on an affine bundle. It is shown that this leads to an affine generalised connection over a prolonged bundle, which is the analogue of what is called a connection of Berwald type in the standard theory of connections. Various new in…

In this work, we are interested in a non symmetric homogeneous space, namely $SO(2m)/Sp(m)$. We show that this space admits a structure of $Z_2^2$-symmetric space. We describe all the non degenerated metrics and classify the Riemannian and Lorentzian ones.

Extends Choi-Wang inequality to Li-Xia affine connections.

This paper proves a curvature entropy inequality for non-symmetric convex bodies.

The paper calculates curvature limits and Gauss-Bonnet theorems in the Heisenberg group.

Geodesic connectedness proved for statistical manifolds with divisible cubic forms.

We give a new characterization of flat affine manifolds in terms of an action of the Lie algebra of classical infinitesimal affine transformations on the bundle of linear frames. We characterize flat affine symplectic Lie groups using symplectic étale affine representations and as a consequence of this, we show that a …

In this paper, we introduce a new structure, namely, affine Szabó connection. We prove that, on $2$-dimensional affine manifolds, the affine Szabó structure is equivalent to one of the cyclic parallelism of the Ricci tensor. A characterization for locally homogeneous affine Szabó surface is obtained. Examples of two- a…

Paper investigates rigidity phenomena for weighted Ricci curvature bounds with Laplacian comparison theorem.

In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connecti…

Classifies meromorphic affine connections on complex surfaces.

In this paper we exhibit a family of flat left invariant affine structures on the double Lie group of the oscillator Lie group of dimension 4, associated to each solution of classical Yang-Baxter equation given by Boucetta and Medina. On the other hand, using Koszul's method, we prove the existence of an immersion of L…

We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of affineness of a generalised connection.

The connection between Jacobi fields and odular structures of affine manifold is established. It is shown that the Jacobi fields generate the natural geoodular structure of affinely connected manifolds.

A geometric structure (FAP-structure), having both absolute parallelism and Finsler properties, is constructed. The building blocks of this structures are assumed to be functions of position and direction. A non-linear connection emerges naturally and is defined in terms of the building blocks of the structure. Two lin…

A special linear Lie group over the real number field and the quarternion field admits a projectivley flat affine connection. We show that parabolic subgroups are autoparallel submanifolds and give a criterion the induced connection is projectively equivalent to a flat affine connection.