Related papers: A method of deforming G-structures
We analyze how gauge fixing, which is required by any practical continuum approach to gauge systems, can interfere with the physical symmetries of such systems. In principle, the gauge fixing procedure, which deals with the (unphysical)…
We study the structure of stationary non equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non…
In this paper, it is presented a methodology to estimate the deformation involved between two objects attending to its physical properties. This methodology can be used, for example, in Computational Vision or Computer Graphics…
This note examines the geometry behind the Hamiltonian structure of isomonodromy deformations of connections on vector bundles over Riemann surfaces. The main point is that one should think of an open set of the moduli of pairs $(V,\nabla)$…
We investigate a relationship between a particular class of two-dimensional integrable non-linear $\sigma$-models and variations of Hodge structures. Concretely, our aim is to study the classical dynamics of the $\lambda$-deformed $G/G$…
We first review the notion of a $G_2$-manifold, defined in terms of a principal $G_2$ ("gauge") bundle over a $7$-dimensional manifold, before discussing their relation to supergravity. In a second thread, we focus on associative…
We explain a construction of $G_2$-instantons on manifolds obtained by resolving $G_2$-orbifolds. This includes the case of $G_2$-instantons on resolutions of $T^7/\Gamma$ as a special case. The ingredients needed are a $G_2$-instanton on…
We investigate the birational geometry of Deligne-Mumford stacks and define new birational invariants in this context.
Topological defects are crucial to the thermodynamics and structure of condensed matter systems. For instance, when incorporated into crystalline membranes like graphene, disclinations with positive and negative topological charge…
A Batalin-Vilkovisky formalism is most general framework to construct consistent quantum field theories. Its mathematical structure is called {\it a Batalin-Vilkovisky structure}. First we explain rather mathematical setting of a…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
A possible scheme of q-deformation, which was recently developed by the present authors, is reviewed by stressing the starting idea.
We consider natural differential operations acting on sections of tensor vector bundles. Arrising problems can be reformulated as invariant theoretical problems (the IT-reduction). We give examples of usage of the IT-reduction. In…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
We apply an integral formula obtained by the author for a general $G$--structure to the case of $G=G_2$. We derive an integral formula relating curvatures and some quadratic invariants of the endomorphism induced by the intrinsic torsion.…
This work deals with a new family of models, which includes the sine-Gordon model and the double-sine-Gordon, triple-sine-Gordon and so on. The investigation is based on a deformation procedure, which is used to deform a well-known model,…
The deformation bicomplex of a module-algebra over a bialgebra is constructed. It is then applied to study algebraic deformations in which both the module structure and the algebra structure are deformed. The cases of module-coalgebras,…
In a recent paper, we have shown that the way of gauge-invariant decomposition of the nucleon spin is not necessarily unique, but there still exists a preferable decomposition from the observational viewpoint. What was not complete in this…
A deformed relativistic kinematics can be understood within a geometrical framework through a maximally symmetric momentum space. However, when considering this kind of approach, usually one works in a flat spacetime and in a curved…
Let f : Y -> X be a morphism of complex projective manifolds, and let F be a subsheaf of the tangent bundle which is closed under the Lie bracket, but not necessarily a foliation. This short paper contains an elementary and very geometric…