arXiv research

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

We study $\mathcal D$-homothetic deformations of almost $α$-Kenmotsu structures. We characterize almost contact metric manifolds which are $CR$-integrable almost $α$-Kenmotsu manifolds, through the existence of a canonical linear connection, invariant under $\mathcal D$-homothetic deformations. If the canonical connect…

Starting from $g$-natural pseudo-Riemannian metrics of suitable signature on the unit tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,\langle,\rangle)$, we construct a family of paracontact metric structures. We prove that this class of paracontact metric structures is invariant under $\mathcal D$-homothetic…

Main interest of the present paper is to investigate the almost α-cosymplectic manifolds for which the characteristic vector field of the almost α-cosymplectic structure satisfies a specific (κ,μ,ν)-nullity condition. This condition is invariant under D-homothetic deformation of the almost cosymplectic (κ,μ,ν)-spaces i…

The aim of this paper is to study Sasakian immersions of compact Sasakian manifolds into the odd-dimensional sphere equipped with the standard Sasakian structure. We obtain a complete classification of such manifolds in the Einstein and $η$-Einstein cases when the codimension of the immersion is $4$. Moreover, we exhib…

The canonical paracontact connection is defined and it is shown that its torsion is the obstruction the paracontact manifold to be paraSasakian. A $\mathcal{D}$-homothetic transformation is determined as a special gauge transformation. The $η$-Einstein manifold are defined, it is prove that their scalar curvature is a …

The paper is a complete study of paracontact metric manifolds for which the Reeb vector field of the underlying contact structure satisfies a nullity condition (the condition \eqref{paranullity} below, for some real numbers $$ and $\tildeμ$). This class of pseudo-Riemannian manifolds, which includes para-Sasak…

We study on which compact Sasakian 3-manifolds the Reeb field, which is a Beltrami field with eigenvalue 2, is an energy minimizer in its adjoint orbit under the action of volume preserving diffeomorphisms. This minimization property for Beltrami fields is relevant because of its connections with the phenomenon of magn…

In this paper we study a special type of metric called *-Ricci soliton on para-Sasakian manifold. We prove that if the para-Sasakian metric is a *-Ricci soliton on a manifold M, then M is either D-homothetic to an Einstein manifold, or the Ricci tensor of M with respect to the canonical paracontact connection vanishes.

Eta-Einstein and $(κ,μ)$-structures studied in dimension 3.

We prove the following results: (i) A Sasakian metric as a non-trivial Ricci soliton is null $η$-Einstein, and expanding. Such a characterization permits to identify the Sasakian metric on the Heisenberg group $\mathcal{H}^{2n+1}$ as an explicit example of (non-trivial) Ricci soliton of such type. (ii) If an $η$-Einste…

Study explores weak generalized K-contact structures in contact metric spaces.

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…

The paper studies $η-$Ricci solitons on contact pseudo-metric manifolds and their properties.

Unified framework for classifying Sasakian, K-contact, and (κ, μ)-manifolds.

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

Study YB operators and their deformations, finding integrable and nontrivial cases.

Smooth deformation of Moishezon manifolds preserves their Moishezon property.

In this paper, we study deformations of holomorphic Poisson maps which extend Horikawa's series of papers on deformations of holomorphic maps in the context of holomorphic Poisson deformations. In appendices, we present deformations of Poisson morphisms in the language of functors of Artin rings which is the algebraic …

In this paper we study the deformation theory of submanifolds characterized by a system of differential forms and provide a criterion for deformations of such submanifolds to be unobstructed. We apply this deformation theory to special Legendrian submanifolds in Sasaki-Einstein manifolds. In general, special Legendrian…

Study on deformations of Lie groupoid morphisms and their properties.

Study canonical deformations of complex forms and their cohomology properties.

In this paper, we study deformations of compact holomorphic Poisson submanifolds which extend Kodaira's series of papers on semi-regularity (deformations of compact complex submanifolds of codimension 1), deformations of compact complex submanifolds of arbitrary codimensions, and stability of compact complex submanifol…

The $L_\infty$-algebra is an algebraic structure suitable for describing deformation problems. In this paper we construct one $L_\infty$-algebra, which turns out to be a differential graded Lie algebra, to control the deformations of Lie algebroids and a second one to control the deformations of Lie subalgebroids. We a…

Study on deformations of holomorphic Cartan geometries, focusing on flat cases.

Study infinitesimal deformations of Lie algebroid pairs.

We study infinitesimal conformal deformations of a triangulated surface in Euclidean space and investigate the change in its extrinsic geometry. A deformation of vertices is conformal if it preserves length cross-ratios. On one hand, conformal deformations generalize deformations preserving edge lengths. On the other h…

The paper studies deformations of Filippov algebroids using cohomology and DGLA.

First non-trivial examples of deformed G_2-instantons, distinguishing nearly parallel G_2-structures.

New spherical curve deformations solve a conjecture.

DeformRS certifies deep networks against various input deformations.

Study deformations of Calabi-Yau foliations using Kuranishi spaces.

Study on bending deformations in hyperbolic manifolds, generalizing Johnson and Millson's work.

The paper studies deformations of cohesive modules on complex manifolds.

We consider some natural infinitesimal Einstein deformations on Sasakian and 3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing spinors and further some integrate to actual Killing spinor deformations. In particular, on 3-Sasakian 7 manifolds these yield infinitesimal Einstein deformations pr…

Study how pairs of 1D foliations can be deformed into contact structures.

Computes spectral Einstein functional for Witten deformation on even-dimensional spin manifolds.

Study geometric properties of S1 singularities and their deformations.

Introducing the deformation theory of holomorphic Cartan geometries, we compute infinitesimal automorphisms and infinitesimal deformations. We also prove the existence of a semi-universal deformation of a holomorphic Cartan geometry.

Develops deformation theory for symplectic foliations using $L_\infty$-algebras.

Study on deformation cohomology for braided commutative structures.

Study on Einstein deformations of negative Kähler Einstein metrics.

In this paper, we study deformations of coisotropic submanifolds in a locally conformal symplectic manifold. Firstly, we derive the equation that governs $C^\infty$ deformations of coisotropic submanifolds and define the corresponding $C^\infty$-moduli space of coisotropic submanifolds modulo the Hamiltonian isotopies.…

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

We consider the stability of Sasaki-extremal metrics under deformations of the complex structure on the Reeb foliation. Given such a deformation preserving the action of a compact subgroup of the automorphism group of a Sasaki-extremal structure, a sufficient condition is given involving the nondegeneracy of the relati…

Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define motions and conformal motions together with deformational decomposition of manifol…

Study strip deformations of hyperbolic polygons with decorated vertices.

In this thesis, we study deformations of compact holomorphic Poisson manifolds and algebraic Poisson schemes in the framework of Kodaira-Spencer's analytic deformation theory and Grothendieck's algebraic deformation theory.