arXiv research

We will consider locally conformally balanced manifolds. We prove that a locally conformally balanced condition is not stable under a small deformation. We prove that locally conformally balanced condition is stable under any proper modification. We prove that symmetric products of the Kodaira surface can be resolve to…

Study locally conformally balanced metrics on specific Lie algebras.

Study non-Kähler metrics on complex nilmanifolds, proving torus structure under certain conditions.

Study on balanced Hermitian structures on Lie algebras twisted by representations.

The abstract discusses conjectures about metrics on complex manifolds.

A Hermitian metric on a complex manifold of complex dimension $n$ is called {\em astheno-Kähler} if its fundamental $2$-form $F$ satisfies the condition $\partial \overline \partial F^{n - 2} =0$. If $n =3$, then the metric is {\em strong KT}, i.e. $F$ is $\partial \overline \partial$-closed. By using blow-ups and the …

Locally conformal SKT structures are introduced and studied on Lie groups and their compact quotients.

Flow stabilizes on non-Kähler metrics near Calabi-Yau.

Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant complex structure J and compatible metric g, which is not required to be invariant. We give classifications of 6-dimensional nilmanifolds M admitting strong Kähler with torsion, balanced or locally conformal Kähler structures (J,g).

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

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

Develops a new representation for constant mean curvature surfaces in hyperbolic 3-space.

We classify both local and global Kähler structures admitting totally geodesic homothetic foliations with complex leaves. The main building blocks are related to Swann's twists and are obtained by applying Weinstein's method of constructing symplectic bundles to Kähler data. As a byproduct we obtain new classes of: hol…

We show that holographic renormalization of relativistic gravity in asymptotically Lifshitz spacetimes naturally reproduces the structure of gravity with anisotropic scaling: The holographic counterterms induced near anisotropic infinity take the form of the action for gravity at a Lifshitz point, with the appropriate …

Conformal-DP improves differential privacy on manifold data by calibrating perturbations based on local densities.

The paper solves a problem related to curvature in complex geometry.

The paper analyzes systoles of complex projective spaces under various metrics.

While the Anomaly flow was originally motivated by string theory, its zero slope case is potentially of considerable interest in non-Kahler geometry, as it is a flow of conformally balanced metrics whose stationary points are precisely Kahler metrics. We establish its convergence on Kahler manifolds for suitable initia…

Study of complex structures on specific solvmanifolds, proving existence and non-existence results.

Proposes SCD-split for CP to balance interpretability and efficiency.

Two-step conformal prediction method for adaptive bounding box uncertainties in multi-object detection.

Characterizes complex Finsler metrics and their properties.

The study identifies assets with local balance deviating from global balance to mitigate financial risk.

The paper explores Hermitian structures on tangent bundles of affine manifolds with Riemannian metrics.

LSB is a new MCMC method for discrete spaces that reduces target evaluations.

Study local diffeomorphisms of conformal circles in pseudo-Riemannian manifolds.

We consider several transformation groups of a locally conformally Kähler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally conformally hyperkähler nor a diagonal Hopf manifold are Killing, holomorphic and th…

New compact examples of pseudo-Kähler manifolds with essential conformal transformations found.

We obtain an example of a compact locally conformal symplectic nilmanifold which admits no locally conformal Kähler metrics. This gives a new positive answer to a question raised by L. Ornea and M. Verbitsky.

In this paper, we study the blow-up of a locally conformal symplectic manifold.We show that there exists a locally conformal symplectic structure on the blow-up of a locally conformal symplectic manifold along a compact induced symplectic submanifold.

Paper characterizes a special hypersurface in 5D sphere.

Motivated by analogous results in locally conformal symplectic geometry, we study different classes of G$_2$-structures defined by a locally conformal closed 3-form. In particular, we give a complete characterization of invariant exact locally conformal closed G$_2$-structures on simply connected Lie groups, and we pre…

We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct locally conformally symplectic structures on compact quotients of all four-dimensional connected and simply connected solvable Lie groups.

We study complex non-Kähler manifolds with Hermitian metrics being locally conformal to metrics with special cohomological properties. In particular, we provide examples where the existence of locally conformal holomorphic-tamed structures implies the existence of locally conformal Kähler metrics, too.

A novel clustering method uses torque balance to group objects.

It is proved that every locally conformal flat Riemannian manifold all of whose Jacobi operators have constant eigenvalues along every geodesic is with constant principal Ricci curvatures. A local classification (up to an isometry) of locally conformal flat Riemannian manifold with constant Ricci eigenvalues is given i…

Constructs metrics with negative curvature on specific manifold types.

We study a fully nonlinear flow for conformal metrics. The long-time existence and the sequential convergence of flow are established for locally conformally flat manifolds. As an application, we solve the $\sk$-Yamabe problem for locally conformal flat manifolds when $k \neq n/2$.

MD-split+ creates locally valid prediction regions for complex data.

Extends moment map concept to locally conformally Kähler manifolds.

This work extends locally conformal analysis to multi-Hamiltonian settings, providing new geometric structures and Hamiltonian dynamics.

Study of Lorentzian manifolds with specific transformations.

We show that locally conformally flat quasi-Einstein manifolds are globally conformally equivalent to a space form or locally isometric to a $pp$-wave or a warped product.

In this note we study the conformal metrics of constant $Q$ curvature on closed locally conformally flat manifolds. We prove that for a closed locally conformally flat manifold of dimension $n\geq 5$ and with Poincarë exponent less than $\frac {n-4}2$, the set of conformal metrics of positive constant $Q$ and positive …

A local classification of the Hermitian manifolds with flat associated connection is given. Hermitian manifolds admitting locally a conformal metric with flat associated connection are characterized by a curvature identity. Locally conformal Kaehler manifolds as well as Hermitian surfaces with vanishing associated conf…

In this paper a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group $\mathbb H_3$, or its conformal classification coincides with the metric one…

Yamabe flow proves compactness of certain locally conformally flat manifolds with positive Ricci curvature.

The paper explores conformal groups on plane waves and proves a conjecture in locally homogeneous settings.