arXiv research

New structure with B-metric extends classical almost contact structures.

In this article, we study an almost contact metric structure on a $G_2$-manifold constructed by Arikan, Cho and Salur in via the classification of almost contact metric structures given by Chinea and Gonzalez. In particular, we characterize when this almost contact metric structure is cosymplectic and narrow down the p…

Study geometric structures and their interactions under different metrics.

The study explores new metric structures on manifolds, linking them to Einstein metrics.

Study shows compact Vaisman manifolds cannot have certain special Hermitian metrics.

We discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical weak Finsler structure, which we call its tautological weak Finsler structure. We compute distances in the tautological weak Finsler structure of a domain and we …

We study almost contact metric structures induced by 2-fold vector cross products on manifolds with $G_2$ structures. We get some results on possible classes of almost contact metric structures. Finally we give examples.

The study of harmonicity for almost contact metric structures was initiated by Vergara-Díaz and Wood and continued by González-Dávila and the present author. By using the intrinsic torsion and some restriction on the type of almost contact metric structure, González-Dávila and the present author have characterised harm…

Characterizes invariant contact metric structures on tangent sphere bundles of compact symmetric spaces.

We consider a $3$-dimensional differentiable manifold with two circulant structures -- a Riemannian metric and an additional structure, whose third power is the identity. The structure is compatible with the metric such that an isometry is induced in any tangent space of the manifold. Further, we consider an associated…

New extremal Kähler metrics found on 4-manifolds with U(2) symmetry.

Characterizes metrics on Lie groups, proving non-simultaneous existence of balanced and pluriclosed metrics.

This article classifies closed G2-structures such that the induced metric is conformally flat. It is shown that any closed G2-structure with conformally flat metric is locally equivalent to one of three explicit examples. In particular, it follows from the classification that any closed G2-structure inducing a metric t…

Study of Calabi-Yau manifold degenerations near complex structure limits.

Geometric flows study nearly parallel G2-structures on 3-Sasakian 7-manifolds.

Study local structure of Einstein metrics with boundary conditions.

Survey of weak metric f-manifolds, generalizing K. Yano's structures.

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

The paper finds the Finsler structure of Apollonian weak metric on unit disc.

We introduce the notion of contact pair structure and the corresponding associated metrics, in the same spirit of the geometry of almost contact structures. We prove that, with respect to these metrics, the integral curves of the Reeb vector fields are geodesics and that the leaves of the Reeb action are totally geodes…

Study of spheres and circles on a manifold with a specific metric structure.

Defines special Joyce structures for ASK manifolds encoding real HK structures.

The paper explores generalized Riemannian manifolds with weak metric structures.

Defines compatibility between Jacobi structures and pseudo-Riemannian metrics on Jacobi algebroids.

In this paper we deal with two classes of mixed metric 3-structures, namely the mixed 3-Sasakian structures and the mixed metric 3-contact structures. Firstly we study some properties of the curvature of mixed 3-Sasakian structures, proving that any manifold endowed with such a structure is Einstein. Then we prove the …

Researchers found all invariant contact structures on tangent sphere bundles of compact symmetric spaces.

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…

Analyzes properties of Hopf manifolds from analytic and metric perspectives.

Study approximates sub-Riemannian structures with Riemannian metrics and analyzes spectral convergence.

This paper explores integrability conditions for generalized metrics and structures on manifolds.

Study of metrics on a specific Lie group with complex structure.

It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost hypercomplex manifold with Hermitian-Norden metrics. It is proven that the introduced mani…

Study balanced Hermitian structures on almost abelian Lie algebras, classifying six-dimensional cases.

The paper adapts metrics to anti-de Sitter structures, characterizing their degeneracies.

Integrable hypercomplex structures with Hermitian and Norden metrics on Lie groups of dimension 4 are considered. The corresponding five types of invariant hypercomplex structures with hyper-Hermitian metric, studied by M.L. Barberis, are constructed here. The different cases regarding the signature of the basic pseudo…

Study relates Finsler structures to Clifford bundles for flat metrics.

Study classifies metrics on anti-de Sitter spacetime with specific symmetries.

The paper constructs almost para-Kähler-Einstein metrics on cotangent bundles.

We prove that any contact metric $(κ,μ)$-space $(M,ξ,φ,η,g)$ admits a canonical paracontact metric structure which is compatible with the contact form $η$. We study such canonical paracontact structure, proving that it verifies a nullity condition and induces on the underlying contact manifold $(M,η)$ a sequence of com…

The paper defines $η$-normality for contact and paracontact manifolds and explores their properties.

Introduces a new geometric structure for statistical manifolds with degenerate metrics.

Study para-complex structures on specific Lie groups, finding explicit forms and properties.

Study of a metric on cotangent bundle spaces of Kähler quotients.

Construct quaternionic-Kähler metrics from special Kähler manifolds with specific BPS structure variations.

In this paper, we consider half-flat $SU(3)$-structures and the subclasses of coupled and double structures. In the general case we show that the intrinsic torsion form $w_1^-$ is constant in each of the two subclasses. We then consider the problem of finding half-flat structures inducing Einstein metrics on homogeneou…

Along the Ricci flow, we study the polyhomogeneity of complete Riemannian metrics endowed with "a Lie structure fibred at infinity", that is, a class of Lie structures at infinity that induce in a precise way a fibre bundle structure on a certain compactification by a manifold with corners. When the compactification is…

On a manifold with an almost contact metric structure $(\varphi,\vecξ,η,g,X,D)$ the notions of the interior and the $N$-prolonged connections are introduced. Using the $N$-prolonged connection, a new almost contact metric structure is defined on the distribution $D$. The properties of this structure are studied.

We introduce a new notion of a homogeneous pair for a pseudo-Riemannian metric $g$ and a positive function $f$ on a manifold $M$ admitting a free $\mathbb{R}_{>0}$-action. There are many examples admitting this structure. For example, (a) a class of pseudo-Hessian manifolds admitting a free $\mathbb{R}_{>0}$-action and…