arXiv research

The 2-parameter family of certain homogeneous Lorentzian 3-manifolds which includes Minkowski 3-space and anti-de Sitter 3-space is considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family has a solvable Lie group structure with left invariant metric. A generalized integral representation formula wh…

A characterization of maximal domains of existence of adapted complex structures for Riemannian homogeneous manifolds under certain extensibility assumptions on their geodesic flow is given. This is applied to generalized Heisenberg groups and naturally reductive Riemannian homogeneous spaces. As an application it is s…

Totally nondegenerate surfaces in CR dimension one are maximally homogeneous and standard.

An almost para-CR structure on a manifold $M$ is given by a distribution $HM \subset TM$ together with a field $K \in Γ({\rm End}(HM))$ of involutive endomorphisms of $HM$. If $K$ satisfies an integrability condition, then $(HM,K)$ is called a para-CR structure. The notion of maximally homogeneous para-CR structure of …

Study shows momentum-based optimizers like Muon and MomentumGD bias towards KKT points in smooth homogeneous models.

Classifies homogeneous CR hypersurfaces in low dimensions with maximal symmetry.

Study how regularization and optimization affect margin in deep models.

Study finds maximal symmetry groups for CR structures with specific properties.

Study Einstein metrics on aligned homogeneous spaces with maximal third Betti number.

Anosov subgroup equidistributes geodesics and holonomies on homogeneous spaces.

Study on CR structures in 7D, proving maximal symmetry dimension.

Study on invariant anti-quasi-Sasakian structures on compact manifolds.

Gradient descent in neural networks maximizes margin.

GD iterates for non-homogeneous deep nets increase margin and converge in direction.

We classify all compact simply connected homogeneous CR manifolds $M$ of codimension one and with non-degenerate Levi form up to CR equivalence. The classification is based on our previous results and on a description of the maximal connected compact group $G(M)$ of automorphisms of $M$. We characterize also the standa…

Classifies 5D homogeneous geometries with nontrivial reducible linear isotropy.

Solves equivalence problem for CR geometries with simple models.

The study finds that certain curved manifolds can be mapped to symmetric spaces.

The Laplace spectrum uniquely identifies five out of eight metrically maximal three-dimensional geometries.

In this work we study the existence of homogeneous Einstein metrics on the total space of homogeneous fibrations such that the fibers are totally geodesic manifolds. We obtain the Ricci curvature of an invariant metric with totally geodesic fibers and some necessary conditions for such a metric to be Einstein in terms …

In this paper, we study the positive cross curvature flow on locally homogeneous 3-manifolds. We describe the long time behavior of these flows. We combine this with earlier results concerning the asymptotic behavior of the negative cross curvature flow to describe the two sided behavior of maximal solutions of the cro…

Study Kähler-Ricci flow on rational homogeneous varieties using algebraic geometry and representation theory.

Let $G$ be a compact connected Lie group and $H$ a closed subgroup of $G$. Suppose the homogeneous space $G/H$ is effective and has dimension 3 or higher. Consider a $G$-invariant, symmetric, positive-semidefinite, nonzero (0,2)-tensor field $T$ on $G/H$. Assume that $H$ is a maximal connected Lie subgroup of $G$. We p…

Researchers study metrics with maximal Ricci curvature on homogeneous spaces.

The study examines the independence of GKM manifolds and symmetric spaces.

The paper introduces new uniformity and homogeneity concepts for Cosserat media.

Classifies special quartic curves up to equivalence.

We bring new insights into the long-standing Alekseevskii conjecture, namely that any connected homogeneous Einstein manifold of negative scalar curvature is diffeomorphic to a Euclidean space, by proving structural results which are actually valid for any homogeneous expanding Ricci soliton, and generalize many well-k…

We present a maximally supersymmetric IIB string background. The geometry is that of a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous five-form flux. We give the explicit supergravity solution, compute the isometries, the 32 Killing spinors, and the symmetry superalgebra, and then d…

All known examples of homogeneous Einstein metrics of negative Ricci curvature can be realized as left-invariant Riemannian metrics on solvable Lie groups. After defining a notion of maximal symmetry among left-invariant Riemannian metrics on a Lie group, we prove that any left-invariant Einstein metric of negative Ric…

Effective estimates for lattice orbits in homogeneous spaces.

Let G be a compact, semi-simple Lie group and H a maximal rank reductive subgroup. The irreducible representations of G can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space G/H twisted by bundles associated to the irreducible, possibly projective, representations of…

Study bifurcations and local rigidity on flag manifolds for Yamabe solutions.

This paper is concerned with properties of maximal solutions of the Ricci and cross curvature flows on locally homogeneous three-manifolds of type SL(2,R). We prove that, generically, a maximal solution originates at a sub-Riemannian geometry of Heisenberg type. This solves a problem left open in earlier work by two of…

The authors give a short survey of previous results on $δ$-homogeneous Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with non-negative sectional curvature, which properly includes the class of all normal homogeneous Riemannian manifolds. As a continuation and an application of these resul…

We prove that a maximal totally complex submanifold $N^{2n}$ of the quaternionic projective space $\mathbb{H}\mathbb{P}^n$ ($n\geq 2$) is a parallel submanifold, provided one of the following conditions is satisfied: (1) $N$ is the orbit of a compact Lie group of isometries, (2) the restricted normal holonomy is a prop…

Upper bounds on Einstein metrics on homogeneous spaces.

The study explores deformations of standard locally homogeneous spaces.

Study of homogeneous spacetimes with isotropic symmetry and their symmetries.

Study path geometries with constant torsion and cone structures.

Study homogeneous Lorentzian manifolds under reductive Lie groups, reducing descriptions to semisimple groups.

New algorithm optimizes complex model selection for non-homogeneous hidden Markov models.

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

The study explores maximal symmetry in Ricci solitons on Lie groups.

Classifies isotropic homogeneous spacetimes for various dimensions.

Study on horospheres in higher rank homogeneous spaces, proving density properties.

In this note we prove the following three algebraic facts which have applications in the theory of holonomy groups and homogeneous spaces: Any irreducibly acting connected subgroup $G \subset Gl(n,\rr)$ is closed. Moreover, if $G$ admits an invariant bilinear form of Lorentzian signature, $G$ is maximal, i.e. it is con…

Maximizing withdrawal success in a pooled annuity fund with multiple annuitants.