arXiv research

Inverts operators near parallel Ricci metric on non-compact manifolds.

The study identifies types of manifolds using variational formulas and integral-differential formulas.

New metrics with special curvature properties are shown to be parallel in certain Lie groups.

The paper classifies special Riemannian manifolds with cyclic parallel Ricci tensor.

We descrive examples of metrics in the conformal class $[g]$ on complete conformally flat Riemannian manifolds $(M,g].$ These metrics have a constant scalar curvature and an harmonic curvature with non parallel Ricci tensor.

Let $(M,g)$ be a compact riemannian manifold without boundary., with parallel Rici curvature. We show that some operators, affine relatively to the Ricci curvature,are locally invertible, near the metric $g$

Special Liouville metrics with Ricci-like conditions are determined by elliptic functions.

Piecewise flat curvatures and flows derived from simplicial structures converge to smooth values.

Paper classifies Einstein-type manifolds with parallel Ricci tensor.

The study classifies gradient Ricci solitons with specific vector fields.

Study shows almost conformal isometry between Sub-Semi-Riemannian metrics and solves a Ricci equation.

New criterion for Ricci-flat manifolds with non-vanishing Rosenberg index.

The paper studies $f$-stability of hypersurfaces in gradient Ricci solitons.

Entropy defined for submanifolds; applies to mean curvature flow limits of surfaces.

Study pp-waves with lightlike parallel spinors in vacuum spacetimes.

Stability and rigidity of Ricci-flat ALE manifolds proven.

A. Derdzinki [D] gave examples of Riemannian metrics with harmonic curvature and non parallel Ricci tensor on some compact manifolds $(M,g]$ . We examine their existence as well as their number wich naturally depends on the geometry of the manifolds.

Study on Ricci-like solitons on specific geometric manifolds, finding properties and conditions.

Study classifies 3D Einstein manifolds with cyclic Ricci tensor.

The paper studies curvature identities and solitons on Spin(7)-manifolds.

The paper proves rigidity of submanifolds in space forms with certain curvature conditions.

The paper studies parallel spinor flows on 3D Cauchy hypersurfaces and provides initial data characterizations.

Study of $η$-Ricci solitons on Kenmotsu 3-manifolds.

Study H-type foliations in sub-Riemannian geometry.

Study Brownian motion on Perelman's almost Ricci-flat manifold, proving convergence to Ricci flow limits.

Study submanifolds in curved spaces with specific curvature bounds.

I apply the algebraic classification of self-adjoint endomorphisms of ${\bf R}^{2,2}$ provided by their Jordan canonical form to the Ricci curvature tensor of four-dimensional neutral manifolds and relate this classification to an algebraic classification of the Ricci curvature spinor. These results parallel similar re…

The paper pinches curvature in expanding Ricci solitons.

In this paper we obtain a simple upper bound for the infimum of the Ricci curvatures of a complete Riemannian manifold with nonzero injectivity radius i(M) depending only on of the i(M). In case of rigidity the Riemannian manifold must be an Euclidean sphere(Euclidean space) conform the injectivity radius be finite(inf…

Study on Kähler Finsler manifolds with curvature bounds, proving theorems.

In this paper we deal with quadratic metric-affine gravity, which we briefly introduce, explain and give historical and physical reasons for using this particular theory of gravity. Further, we introduce a generalisation of well known spacetimes, namely pp-waves. A classical pp-wave is a 4-dimensional Lorentzian spacet…

The Eisenhart problem of finding parallel tensors treated already in the framework of quasi-constant curvature manifolds in \cite{x:j} is reconsidered for the symmetric case and the result is interpreted in terms of Ricci solitons. If the generator of the manifold provides a Ricci soliton then this is i) expanding on p…

The paper classifies metrics on Heisenberg group's cotangent bundle.

Study curvature properties of $G_2$ connections with skew-symmetric torsion.

Study improves eigenvalue bounds on Kähler manifolds.

Investigates curvature properties of generalized pp-wave metric.

The curvature properties of a specific type of 6-manifold are explored.

In this paper we obtain a splitting theorem for the symmetric diffusion operator $Δ_φ=Δ-\left<\nablaφ,\nabla \right>$ and a non-constant $C^3$ function $f$ in a complete Riemannian manifold $M$, under the assumptions that the Ricci curvature associated with $Δ_φ$ satisfies ${\rm Ric}_φ(\nabla f,\nabla f)\ge 0$, that $|…

Investigates curvature properties of Robinson-Trautman metric.

Study minimal graphs on non-negative Ricci curvature manifolds.

Study on pseudo-Riemannian metrics on Lie groups, finding new non-Einstein examples.

The paper examines conditions of parallelism for a special tensor on 3D hypersurfaces.

The paper studies para-Kenmotsu manifolds and their properties.

The paper proves a gap theorem for almost non-negatively curved manifolds.

Uniqueness of asymptotic limits for Ricci-flat manifolds with linear volume growth is proven.

In this work we consider periodic spherically symmetric metrics of constant positive scalar curvature on the n-dimensional cylinder called pseudo-cylindric metrics. These metrics belong to the conformal class $[g_0]$ of the Riemannian product $S^1\times S^{n-1}$ : a circle of length $T$ crossed with the (n-1)-dimension…

Study torsion and curvature in ACYT and AHKT 8-manifolds.

The paper proves unique properties of Riemannian twistor spaces under specific curvature conditions.