arXiv research

Study weakly weighted Einstein-Finsler metrics, showing specific curvature properties and characterizing them.

The study examines weakly Einstein metrics on specific types of manifolds.

The paper classifies weakly Einstein critical metrics on compact manifolds with boundary.

The study examines weakly Einstein Lie groups and proves non-existence for certain types.

Weakly Einstein Kähler surfaces are characterized and classified.

New examples of weakly Einstein conformal products are constructed.

Classifies weakly Einstein hypersurfaces in spaces of constant curvature.

Study on metric properties near boundary of tube domains.

Classifies weakly Einstein submanifolds in space forms satisfying specific equalities.

Extends construction of Kähler-Einstein metrics to noncompact manifolds.

Classifies weakly Einstein curvature tensors in 4D Euclidean space.

Extends classical stability results to new geometric settings.

We study Kahler surfaces with harmonic anti-selfdual Weyl tensor. We provide an explicit local description, which we use to obtain the complete classification in the compact case. We give new examples of extremal Kahler metrics, including Kahler-Einstein metrics and conformally Einstein Kahler metrics. We also extend s…

The study characterizes and classifies specific types of manifolds using conformal and quasi-Einstein properties.

Let (M, g) be a compact Einstein manifold with non-empty boundary. We prove that Killing fields at the boundary extend to Killing fields of any (M, g) provided the boundary is weakly convex and a simple condition on the fundamental group holds. This gives a new proof of the classical infinitesimal rigidity of convex su…

Schur theorem proven for weakly Landsberg Finsler metrics.

A weakly Einstein manifold is a generalization of a 4-dimensional Einstein manifold, which is defined as an application of a curvature identity derived from the generalized Gauss-Bonnet formula for a 4-dimensional compact oriented Riemannian manifold. In this paper, we shall give a characterization of a weakly Einstein…

The paper studies weighted Ricci curvatures and characterizes Randers metrics.

The paper proves a conjecture about the Bergman metric of real analytic domains.

The present paper deals with the proper existence of a generalized class of recurrent manifolds, namely, hyper-generalized recurrent manifolds. We have established the proper existence of various generalized notions of recurrent manifolds. For this purpose we have presented a metric and computed its curvature propertie…

Study Einstein Lie groups and geodesic orbit manifolds, finding some are not geodesic orbit.

Derives local forms for Bochner-flat (pseudo-)Kähler metrics.

The study proves the non-existence of certain Kähler metrics with specific curvature properties.

We compute global log canonical thresholds of a large class of quasismooth well-formed del Pezzo weighted hypersurfaces in $\mathbb{P}(a_{1},a_{2},a_{3},a_{4})$. As a corollary we obtain the existence of orbifold Kähler--Einstein metrics on many of them, and classify exceptional and weakly exceptional quasismooth well-…

We review recent work on the Einstein equations of general relativity when the curvature is defined in a weak sense. Weakly regular spacetimes are constructed, in which impulsive gravitational waves, as well as shock waves, propagate.

Under weak regularity assumptions, only, we develop a fully geometric theory of vacuum Einstein spacetimes with T2 symmetry, establish the global well-posedness of the initial value problem for Einstein's field equations, and investigate the global causal structure of the constructed spacetimes. Our weak regularity ass…

Study of caustics in Einstein-dust system, showing spacetime singularities and diverging curvature.

We introduce the notion of a hamiltonian 2-form on a Kaehler manifold and obtain a complete local classification. This notion appears to play a pivotal role in several aspects of Kaehler geometry. In particular, on any Kaehler manifold with co-closed Bochner tensor, the (suitably normalized) Ricci form is hamiltonian, …

Study on generalized $m$-Kropina metrics in modified gravity and cosmology.

The paper examines Randers metrics with isotropic scalar curvature properties.

We consider the Einstein-Maxwell-fluid constraint equations, and make use of the conformal method to construct and parametrize constant-mean-curvature hyperboloidal initial data sets that satisfy the shear-free condition. This condition is known to be necessary in order that a spacetime development admit a regular conf…

Suppose $(X,J,ω)$ is a Fano manifold and $t \to r_t$ is a diverging Kähler-Ricci trajectory. We construct a bounded geodesic ray $t \to u_t$ weakly asymptotic to $t \to r_t$, along which Ding's $\mathcal F$-functional decreases, partially confirming a folklore conjecture. In absence of non-trivial holomorphic vector fi…

Study properties of Kenmotsu manifolds with a specific connection.

This paper explores new Finsler metrics and their connections to generalized Sakaguchi's Theorem.

Study on polyhedra rigidity, finding non-existence of flexible weakly convex decomposable polyhedra.

Study shows expanding Ricci solitons from specific metric cones.

In this paper, we prove rigidity results on gradient shrinking Ricci solitons with weakly harmonic Weyl curvature tensors. Let $(M^n, g)$ be a compact gradient shrinking Ricci soliton satisfying ${\rm Ric}_g + Ddf = ρg$ with $ρ>0$ constant. We show that if $(M,g)$ satisfies $δ\mathcal W (\cdot, \cdot, \nabla f) = 0$, t…

Study critical metrics on Riemannian manifolds, finding new minimizers and rigidity results.

Let L be a holomorphic line bundle with a positively curved singular Hermitian metric over a complex manifold X. One can define naturally the sequence of Fubini-Study currents associated to the space of square integrable holomorphic sections of the p-th tensor powers of L. Assuming that the singular set of the metric i…

Study on special Finsler metrics with conditions for Riemannian and isotropic properties.

Considering the class G of g-natural metrics on the tangent bundle of a Riemannian manifold (M, g), it is shown that the flatnees for g is a necessary and sufficient condition of weakly symmetry (recurrent or pseudo-symmetry) of G. In particular, the cases of weakly symmetric Sasakian lift metric studied by Bejan and C…

The paper classifies closed Einstein manifolds with specific curvature properties.

Characterizes and simplifies $m$-th root Finsler metrics.

Paper solves open problem in complex Finsler geometry.

New contact structures on spheres and tori with weakly compatible metrics.

Sharp bounds derived for eigenvalues on specific geometric spaces.

The paper studies conformally flat cubic metrics with isotropic curvature, finding they must be Minkowski.

Bismut Einstein metrics on complex manifolds are Kähler Einstein or Bismut Ricci flat.