arXiv research

Geometrically deforms $L_\infty$ algebras to Lie algebroids, revealing new invariants.

Study geometric properties of S1 singularities and their deformations.

Maps geometric deformations to algebraic classes in Lie groupoids and algebroids.

Geometric deformations preserve post-Lie algebra structure in regularity structures.

Geometric study of cuspidal $S_1$ singularities using diffeomorphisms and isometries.

We shall develop a new deformation theory of geometric structures in terms of closed differential forms. This theory is a generalization of Kodaira -Spencer theory and further we obtain a criterion of unobstructed deformations. We apply this theory to certain geometric structures: Calabi-Yau, HyperKähler, $\G$ and $\Sp…

The paper classifies quantizable functions and explores symmetry in quantization methods.

In this article we give the realization of the Klein's Program for geometrical structures (Riemannian spaces and fiber bundles with connection) with arbitrary variable curvature within the framework of infinite deformed groups. These groups generalize gauge groups to the case of nontrivial action on the base space of b…

We give a brief overview of the current state of the study of the deformation theory of Kleinian groups. The topics covered include the definition of the deformation space of a Kleinian group and of several important subspaces; a discussion of the parametrization by topological data of the components of the closure of …

Study on solitons in deformed Kenmotsu manifolds with specific vector fields.

Study of $q$-rationals and their geometric properties, including deformed Farey triangulation and Springborn operations.

New method for quantizing symplectic manifolds with Lagrangian bundles.

A notion of geometric formality in the context of Bott-Chern and Aeppli cohomologies on a complex manifold is discussed. In particular, by using Aeppli-Bott-Chern-Massey triple products, it is proved that geometric Aeppli-Bott-Chern formality is not stable under small deformations of the complex structure.

Study geometric structures on LVM threefolds, focusing on resonant structures.

Geometric interpretation of 2d-4d wall-crossing formulas.

Survey on quantization methods on Kähler manifolds.

Extensions of the generalized Weierstrass representation to generic surfaces in 4D Euclidean and pseudo-Euclidean spaces are given. Geometric characteristics of surfaces are calculated. It is shown that integrable deformations of such induced surfaces are generated by the Davey -Stewartson hierarchy. Geometrically thes…

Geometric structures modeled on rational homogeneous manifolds are studied to characterize rational homogeneous manifolds and to prove their deformation rigidity. To generalize these characterizations and deformation rigidity results to quasihomogeneous varieties, we first study horospherical varieties and geometric st…

We explain the geometric origin of the $L_{\infty}$-algebra controlling deformations of pre-symplectic structures.

Theory of space-time currents for geometric evolutions.

Bistable structures associated with non-linear deformation behavior, exemplified by the Venus flytrap and slap bracelet, can switch between different functional shapes upon actuation. Despite numerous efforts in modeling such large deformation behavior of shells, the roles of mechanical and nonlinear geometric effects …

Necessary and sufficient conditions for some deformation algebras to provide formal Frobenius structures are given. Also, examples of formal Frobenius structures with fundamental tensor that is not of the deformation type and examples of symmetric non-metric connections are presented.

We present a deformable generator model to disentangle the appearance and geometric information for both image and video data in a purely unsupervised manner. The appearance generator network models the information related to appearance, including color, illumination, identity or category, while the geometric generator…

The paper studies quantization on symplectic manifolds with real polarizations, comparing different quantization methods.

Anosov deformations created for surfaces with specific properties.

We consider the deformation theory of two kinds of geometric objects: foliations on one hand, pre-symplectic forms on the other. For each of them, we prove that the geometric notion of equivalence given by isotopies agrees with the algebraic notion of gauge equivalence obtained from the $L_{\infty}$-algebras governing …

Surveying progress on deformed Hermitian-Yang-Mills equation and its connections to stability.

Study on deformation of weighted scalar curvature, proving geometric results and stability.

A purely combinatorial compactification of the configuration space of n (>4) distinct points with equal weights in the real projective line was introduced by M. Yoshida. We geometrize it so that it will be a real hyperbolic cone-manifold of finite volume with dimension n-3. Then, we vary weights for points. The geometr…

Study normal bundle and deformation to get new pushforward maps.

Geometric interpretation of Fock-Goncharov positivity and disk stabilization in symmetric space.

We prove that the Kupershmidt deformation of a bi-Hamiltonian system is itself bi-Hamiltonian. Moreover, Magri hierarchies of the initial system give rise to Magri hierarchies of Kupershmidt deformations as well. Since Kupershmidt deformations are not written in evolution form, we start with an outline a geometric fram…

In this paper we expose on the dual 1-jet space J^{1*}(R,M^4) the distinguished (d-) Riemannian geometry (in the sense of d-connection, d-torsions, d-curvatures and some gravitational-like and electromagnetic-like geometrical models) for the (t,x)-conformal deformed Berwald-Moor Hamiltonian metric of order four.

Study higher rank deformed Hermitian-Yang-Mills equations for stable vector bundles.

The paper classifies deformations of curves with inflections and vertices.

The paper quantizes Hessian structures on R^2 using KV-algebras.

We extend to the conformal realm the concept of genuine deformations of submanifolds, introduced by Dajczer and the first author for the isometric case. Analogously to that case, we call a conformal deformation of a submanifold $M^n$ genuine if no open subset of $M^n$ can be included as a submanifold of a higher dimens…

A mathematical model describes deforming manifolds with precise vectors and fields.

Geometric models for algebraic suspensions using affine deformation spaces.

Study compares geometric approaches for shape and deformation statistics.

Quantum neural networks need both data-dependent and trainable unitaries for effective geometric deformation.

This article gives an exposition of the deformation theory for pairs $(X, E)$, where $X$ is a compact complex manifold and $E$ is a holomorphic vector bundle over $X$, adapting an analytic viewpoint à la Kodaira-Spencer. By introducing and exploiting an auxiliary differential operator, we derive the Maurer--Cartan equa…

A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kaehler structure is proposed. The Hilbert space of states is realized via the Bott-Borel-Weil theorem in the sheaf cohomology of the geometric quantization line bundle. The correspondin…

The paper connects isomonodromic and isospectral deformations for $\mathfrak{sl}_2(\mathbb{C})$ connections.

Study shows how to deform foliated manifolds with flat leaves, leading to geometric characterization.

The study extends Dehn filling to Lie groups, ensuring geometric properties.

Here (the last paper in a series of four) we end our presentation of the basics of a systematical approach to the differential geometry of a smooth manifold M (supporting a metric field g and a general connection del) which uses the geometric algebras of multivector and extensors (fields) developed in previous papers. …

New findings on complex manifold properties under deformations.