arXiv research

We study the Hamiltonian formalisms of the second order degenerate Clèment and Sarıoğlu-Tekin Lagrangians. The Dirac-Bergmann constraint algorithm is employed while arriving at the total Hamiltonian functions and the Hamilton's equations on the associated momemtum phase spaces whereas the Gotay-Nester-Hinds algorithm i…

An optimal control problem associated with the dynamics of the orientation of a bipolar molecule in the plane can be understood by means of tools in differential geometry. For first time in the literature $k$-symplectic formalism is used to provide the optimal control problems associated to some families of partial dif…

Unified geometric formulation of Maxwell-Vlasov system using presymplectic and symmetry reduction.

In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we deduce an intrinsic framework for this type of dynamical systems. Interesting appli…

The aim of this paper is to propose an unambiguous intrinsic formalism for higher-order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, which implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geo…

Establishes Poincaré's lemma for formal manifolds.

Foundations laid for formal manifolds in differential geometry.

Explores local structure of morphisms and formal submanifolds in formal manifolds theory.

Study non-formal pseudo-differential operators over formal ones.

The isotropy action on certain symmetric spaces is shown to be equivariantly formal.

Strong formal properties for toric and homogeneous Kähler manifolds.

A metric is formal if all products of harmonic forms are again harmonic. The existence of a formal metric implies Sullivan formality of the manifold, and hence formal metrics can exist only in presence of a very restricted topology. We show that a warped product metric is formal if and only if the warping function is c…

The study shows strong formality in certain complex manifolds.

Formal manifolds with non-negative Ricci curvature have formal covers.

New hierarchies derived from KP hierarchy using non-formal operators and Yang-Mills action.

Extended equivariant BV formalism to manifolds with boundaries.

We define the notion of a formal connection for a smooth family of star products with fixed underlying symplectic structure. Such a formal connection allows one to relate star products at different points in the family. This generalizes the formal Hitchin connection introduced by the first author. We establish a necess…

Defines formal exponentials for graded manifolds and linearizes QP-manifolds.

Formality of Dolbeault DGAs on complex nilmanifolds restricted to tori.

Study on geometrically formal metrics on complex manifolds.

Research on formality problem for special holonomy manifolds.

Defines formal vertex laws related to Lie conformal algebras.

Deform quantization recovers scalar curvature in complex structures.

Formal methods verify continuous auctions at exchanges.

We describe a canonical form for linear differential operators that are formally self-adjoint or formally skew-adjoint.

There are solved standard problems related to Formal (Holomorphic) Segre preserving Mappings of non-trivial Real-Formal Hypersurfaces in $\mathbb{C}^{2}$.

Derives localization formulas in Batalin-Vilkovisky formalism.

Proves formal self-adjointness of certain differential operators.

New findings on complex manifold properties under deformations.

A Riemannian manifold is called geometrically formal if the wedge product of harmonic forms is again harmonic, which implies in the compact case that the manifold is topologically formal in the sense of rational homotopy theory. A manifold admitting a Riemannian metric of positive sectional curvature is conjectured to …

We prove that for a fibration of simply-connected spaces of finite type $F\hookrightarrow E\to B$ with $F$ being positively elliptic and $H^*(F,\qq)$ not possessing non-trivial derivations of negative degree, the base $B$ is formal if and only if the total space $E$ is formal. Moreover, in this case the fibration map i…

This paper formalizes manifolds in positive characteristic varieties.

In this paper, we study the formal solution space of a nonlinear PDE in a fiber bundle. To this end, we start with foundational material and introduce the notion of a pfd structure to build up a new concept of profinite dimensional manifolds. We show that the infinite jet space of the fiber bundle is a profinite dimens…

This paper explores formal verification for autonomous systems, identifying limitations and proposing improvements.

We investigate harmonic forms of geometrically formal metrics, which are defined as those having the exterior product of any two harmonic forms still harmonic. We prove that a formal Sasakian metric can exist only on a real cohomology sphere and that holomorphic forms of a formal Kähler metric are parallel w.r.t. the L…

We discuss the question of geometric formality for rationally elliptic manifolds of dimension $6$ and $7$. We prove that a geometrically formal six-dimensional biquotient with $b_{2}=3$ has the real cohomology of a symmetric space. We also show that a rationally hyperbolic six-dimensional manifold with $b_2\leq 2$ and …

We recall the construction of non-formal deformation quantization of the Poincare Group ISO(1,1) on its coadjoint orbit and exhibit the associated non-formal star-exponentials.

An action of a compact Lie group is called equivariantly formal, if the Leray--Serre spectral sequence of its Borel fibration degenerates at the E_2-term. This term is as prominent as it is restrictive. In this article, also motivated by the lack of junction between the notion of equivariant formality and the concept o…

Paper formalizes multi-dimensional FSD using geometric methods.

Introduces formal frames for manifolds and their properties.

New infinite family of hyperbolic L-space knots with specific semigroups.

We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend o…

Formal Normal Form created for special CR singularities.

Machine learning algorithms for prediction are increasingly being used in critical decisions affecting human lives. Various fairness formalizations, with no firm consensus yet, are employed to prevent such algorithms from systematically discriminating against people based on certain attributes protected by law. The aim…

Several large classes of homogeneous spaces are known to be formal---in the sense of Rational Homotopy Theory. However, it seems that far fewer examples of non-formal homogeneous spaces are known. In this article we provide several construction principles and characterisations for non-formal homogeneous spaces, which w…

The article confirms Joyce's examples of G2-holonomy are formal spaces.

Non-formal G2 manifold found with holonomy.

Paper applies Newman-Penrose formalism to ACM manifolds.