arXiv research

Study proves estimate for Hessian quotient equations on 2D Riemannian manifolds.

The paper defines conditions for a Riemannian structure on a symplectic quotient.

The study examines the smoothness of submetries in Riemannian manifolds.

Interior $C^{2}$ estimates for sum Hessian quotient equations on Riemannian manifolds

Establishes a concavity property for positive Hessian quotient operators.

New manifold types defined on quotient spaces.

We prove that the quotient space of a variationally complete group action is a good Riemannian orbifold. The result is generalized to singular Riemannian foliations without horizontal conjugate points.

New formulas for Riemannian gradient and Hessian on manifold metrics.

Characterizes orbifolds with upper curvature bounds as reflectofolds.

Develops arithmetic PDE geometry using Fermat quotients.

Teichmüller space realized as symplectic quotient.

Study shows infinitely many metrics with nonnegative sectional or positive Ricci curvature on specific 5D quotients.

Researchers develop geodesics for a new metric on correlation matrices.

Sub-Riemannian Selberg trace formulae for compact quotients of SL(2, R)

We construct compactifications of Riemannian locally symmetric spaces arising as quotients by Anosov representations. These compactifications are modeled on generalized Satake compactifications and, in certain cases, on maximal Satake compactifications. We deduce that these Riemannian locally symmetric spaces are topol…

The abstract discusses compact quotients of Riemannian products by discrete subgroups, generalizing Inoue-Bombieri surfaces.

Study of 4D symmetric spaces with (2,2) signature.

The study classifies Riemannian manifolds with curvature nullity.

New sub-Riemannian structures fail synthetic curvature bounds.

A new Riemannian framework for robust covariance estimation.

Given a metric space $X$ and a function $f: X \to \mathbb{R}$, the Reeb construction gives metric a space $X_f$ together with a quotient map $X \to X_f$. Under suitable conditions $X_f$ becomes a metric graph and can therefore be used as a graph approximation to $X$. The Gromov-Hausdorff distance from $X_f$ to $X$ is b…

Compact quotients of homogeneous spaces are studied, leading to new findings about sphere bundles.

Rational ellipticity proven for $G$-manifolds with specific quotient properties.

The chapter reviews metrics for comparing curves, focusing on quotient elastic and square root velocity metrics.

Researchers find shortest paths on a special group structure.

We prove existence of regions minimizing perimeter under a volume constraint in contact sub-Riemannian manifolds such that their quotient by the group of contact transformations preserving the sub-Riemannian metric is compact.

The study proves curvature bounds for quotient spaces of isometric actions.

In this paper we give an explicit description of the bounded displacement isometries of a class of spaces that includes the Riemannian nilmanifolds. The class of spaces consists of metric spaces (and thus includes Finsler manifolds) on which an exponential solvable Lie group acts transitively by isometries. The bounded…

Study pseudo-Riemannian Sasaki metrics on solvable Lie groups.

New metrics defined for full-rank correlation matrices, ensuring unique operations.

We study the classification of smooth toroidal compactifications of nonuniform ball quotients in the sense of Kodaira and Enriques. Moreover, several results concerning the Riemannian and complex algebraic geometry of these spaces are given. In particular we show that there are compact complex surfaces which admit Riem…

This article discusses the existence problem of a compact quotient of a symmetric space by a properly discontinuous group with emphasis on the non-Riemannian case. Discontinuous groups are not always abundant in a homogeneous space $G/H$ if $H$ is non-compact. The first half of the article elucidates general machinery …

This article studies the volume of compact quotients of reductive homogeneous spaces. Let $G/H$ be a reductive homogeneous space and $Γ$ a discrete subgroup of $G$ acting properly discontinuously and cocompactly on $G/H$. We prove that the volume of $Γ\backslash G/H$ is the integral, over a certain homology class of $Γ…

We study locally conformally Berwald metrics on closed manifolds which are not globally conformally Berwald. We prove that the characterization of such metrics is equivalent to characterizing incomplete, simply-connected, Riemannian manifolds with reducible holonomy group whose quotient by a group of homotheties is clo…

Paper computes optimal matching between curves on manifolds.

The paper examines gradient Ricci solitons on orbifolds and proves their rigidity properties.

The study explores deformations of discrete subgroups in non-compact homogeneous spaces.

In this article we collect results obtained by the authors jointly with other authors and we discuss old and new ideas. In particular we discuss singularities of the exponential map, completeness and homogeneity for Riemannian Hilbert quotient manifolds. We also extend a Theorem due to Nomizu and Ozeki to infinite dime…

In this paper we construct infinitely many examples of a Riemannian submersion from a simple, compact Lie group $G$ with bi-invariant metric onto a smooth manifold that cannot be a quotient of $G$ by a group action. This partially addresses a question of K. Grove's about Riemannian submersions from Lie groups.

Completes the space of vector-valued one-forms on manifolds.

We show the existence of nonsymmetric homogeneous spin Riemannian manifolds whose Dirac operator is like that on a Riemannian symmetric spin space. Such manifolds are exactly the homogeneous spin Riemannian manifolds $(M,g)$ which are traceless cyclic with respect to some quotient expression $M=G/K$ and reductive decom…

We give some rigidity theorems for an n$(\geq4)$-dimensional compact Riemannian manifold with harmonic Weyl curvature, positive scalar curvature and positive constant $σ_2$. Moreover, when $n=4,$ we prove that a 4-dimensional compact locally conformally flat Riemannian manifold with positive scalar curvature and positi…

Several representations of geometric shapes involve quotients of mapping spaces. The projection onto the quotient space defines two sub-bundles of the tangent bundle, called the horizontal and vertical bundle. We investigate in these notes the sub-Riemannian geometries of these bundles. In particular, we show for a sel…

Near isospectrality forces full isospectrality for compact quotients of symmetric spaces.

We classify representations of compact connected Lie groups whose induced action on the unit sphere has an orbit space isometric to a Riemannian orbifold.

We exhibit examples of compact three-dimensional CR manifolds of positive Webster class, {\em Rossi spheres}, for which the pseudo-hermitian mass as defined in \cite{CMY17} is negative, and for which the infimum of the CR-Sobolev quotient is not attained. To our knowledge, this is the first geometric context on smooth …

Given a compact Lie group, endowed with a bi-invariant Riemannian metric, its complexification inherits a Kaehler structure having twice the kinetic energy of the metric as its potential, and Kaehler reduction with reference to the adjoint action yields a stratified Kaehler structure on the resulting adjoint quotient. …

We develop a theory of reduction for generalized Kahler and hyper-Kahler structures which uses the generalized Riemannian metric in an essential way, and which is not described with reference solely to a single generalized complex structure. We show that our construction specializes to the usual theory of Kahler and hy…