arXiv research

Study finds new factorable surfaces with non-zero curvature in pseudo-Galilean space.

No regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces are found.

Estimates the first non-zero eigenvalue using Ricci curvature on graph edges.

Statistical Lie algebras with constant curvature are linked to locally conformally Kähler structures.

Recently, we developed a method for the study of holonomy properties of non-Riemannian Finsler manifolds and obtained that the holonomy group can not be a compact Lie group, if the Finsler manifold of dimension $> 2$ has non-zero constant flag curvature. The purpose of this paper is to move further, exploring the holon…

The holonomy group $G$ of a pseudo-quaternionic-Kählerian manifold of signature $(4r,4s)$ with non-zero scalar curvature is contained in $\Sp(1)\cdot\Sp(r,s)$ and it contains $\Sp(1)$. It is proved that either $G$ is irreducible, or $s=r$ and $G$ preserves an isotropic subspace of dimension $4r$, in the last case, ther…

The abstract proves properties of Berwald spaces with non-zero flag curvature.

New curvature obstruction for Killing vector fields on Lorentzian manifolds.

Sphere theorems for p-Laplacian eigenvalues established.

The study analyzes weighted manifolds with curvature bounds, proving eigenvalue estimates and inequalities.

We complete the reduction of Sasakian manifolds with the non-zero case by showing that Willett's contact reduced space is compatible with the Sasakian structure. We then prove the compatibility of the non-zero Sasakian (in particular, contact) reduction with the reduction of the Kähler (in particular, symplectic) cone.…

Sharp bounds found for the first non-zero Steklov eigenvalue.

Paper finds bounds for Steklov eigenvalues on manifolds.

For a Riemannian closed spin manifold and under some topological assumption (non-zero $\hat{A}$-genus or enlargeability in the sense of Gromov-Lawson), we give an optimal upper bound for the infimum of the scalar curvature in terms of the first eigenvalue of the Laplacian. The main difficulty lies in the study of the o…

No algebraic 3rd degree hypersurfaces in Euclidean spaces have constant mean curvature.

Metric spaces with non-positive curvature have a specific curve isoperimetric property.

We construct new explicit compact supersymmetric valid solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic equations of motion in dimension six. We present balanced Hermitian structures on compact nilmanifolds in dimension six satisfying the heterotic supersymmetry equations…

We study the 8 natural GL equivariant geometric realization questions for the space of generalized algebraic curvature tensors. All but one of them is solvable; a non-zero projectively flat Ricci antisymmetric generalized algebraic curvature is not geometrically realizable by a projectively flat Ricci antisymmetric tor…

We give an estimate on the lower bound of the first non-zero eigenvalue of the Laplacian for a closed Riemannian manifold with positive Ricci curvature in terms of the in-diameter and the lower bound of the Ricci curvature.

Study on surfaces with constant anisotropic mean curvature in 3D space.

The paper proves the existence of embedded hypersurfaces of constant mean curvature in manifolds with positive Ricci curvature.

Berwald spaces with non-zero flag curvature are Riemannian.

The study examines complete conformally flat submanifolds with nullity in Euclidean space.

Lower bound found for Steklov eigenvalue on curved manifolds.

Along the line of the Yang Conjecture, we give a new estimate on the lower bound of the first non-zero eigenvalue of a closed Riemannian manifold with negative lower bound of Ricci curvature in terms of the in-diameter and the lower bound of Ricci curvature.

Extends Choi-Wang inequality to Li-Xia affine connections.

In [29], Plebanski reformulated the anti-self-dual Einstein equations with non-zero scalar curvature as a first order PDE for a connection in an SO(3)-bundle over the four-manifold. The aim of this article is to place this differential equation in a new framework, in which it is both elliptic and a stationary point of …

In Finsler geometry, there are infinitely many models of constant curvature. The Funk metrics, the Hilbert-Klein metrics and the Bryant metrics are projectively flat with non-zero constant curvature. A recent example constructed by the author is projectively flat with zero curvature. In this paper, we introduce a techn…

We show that complete uniform visibility manifolds of finite volume with sectional curvature $-1 \leq K \leq 0$ have positive simplicial volumes. This implies that their minimal volumes are non-zero.

We prove that rationally essential manifolds with suitably large fundamental groups do not admit any maps of non-zero degree from products of closed manifolds of positive dimension. Particular examples include all manifolds of non-positive sectional curvature of rank one and all irreducible locally symmetric spaces of …

Paper provides lower bounds for eigenvalues on singular Riemannian foliations.

Upper bounds for Steklov eigenvalues on curved submanifolds.

We consider regular surfaces $M$ that are given as the zeros of a polynomial function $p:R^3\rightarrow R$, where the gradient of $p$ vanishes nowhere. We assume that $M$ has non-zero mean curvature and prove that there exist only two examples of such surfaces, namely the sphere and the circular cylinder.

We construct explicit compact supersymmetric solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic string equations in dimension five. We present a quadratic condition on the curvature which is necessary and sufficient the heterotic supersymmetry and the anomaly cancellation t…

The paper provides an intrinsic proof of a theorem about Landsberg spaces.

A map between manifolds is an isometry if it's Lipschitz and scalar curvature bounded.

Study Hamiltonian stationary Lagrangian surfaces in complex space forms.

The paper defines subdifferentials on Hadamard manifolds and identifies conditions for Fenchel conjugate equality.

Example surfaces with curvature bounds but no Laplacian eigenvalue lower bound.

MATLAB toolbox pde2path solves geometric PDEs and finds bifurcations in immersed surfaces.

In this paper we prove some general results on constant mean curvature lamination limits of certain sequences of compact surfaces $M_n$ embedded in $\mathbb R^3$ with constant mean curvature $H_n$ and fixed finite genus, when the boundaries of these surfaces tend to infinity. Two of these theorems generalize to the non…

We demonstrate that every non-tubular channel linear Weingarten surface in Euclidean space is a surface of revolution, hence parallel to a catenoid or a rotational surface of non-zero constant Gauss curvature. We provide explicit parametrizations and deduce existence of complete hyperbolic linear Weingarten surfaces.

Study derives a limit functional for Willmore graphs with curvature penalization.

We characterize biharmonic anti-invariant surfaces in $3$-dimensional generalized $(κ, μ)$-manifolds with non-zero constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of biharmonic submanifolds in a c…

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

The paper classifies surfaces with constant mean curvature and rotational symmetry.

We consider Ricci flow of complete Riemannian manifolds which have bounded non-negative curvature operator, non-zero asymptotic volume ratio and no boundary. We prove scale invariant estimates for these solutions. Using these estimates, we show that there is a limit solution, obtained by scaling down this solution at a…

The paper explores properties of Finsler manifolds with specific curvature conditions.