Paper offers a framework for estimating symmetric properties efficiently.
problem Estimating symmetric properties of distributions from samples.
method General framework using profile maximum likelihood (PML) distribution.
result Optimal sample complexity for many properties, practical algorithms.
Study non-symmetric non-metric connections on Kenmotsu manifolds.
problem Properties of Kenmotsu manifolds with non-symmetric non-metric connections.
method Investigate curvature properties and irregularity of Kenmotsu manifolds.
result Kenmotsu manifolds with non-symmetric non-metric connections are irregular.
Causal properties of Lorentzian symmetric spaces are investigated in the paper. The global hyperbolicity of the Cahen--Wallach Lorentzian symmetric spaces is proved.
Geodesic orbit and weakly symmetric properties in spray geometry.
problem Understanding properties of homogeneous spray manifolds.
method Using reductive decompositions and spray vector fields to describe and prove properties.
result Weakly symmetric spray manifolds are geodesic orbit manifolds.
Study properties of semi-symmetric Lorentzian spaces, foliated manifolds.
problem Properties of semi-symmetric pseudo-Riemannian manifolds.
method Investigate foliated manifolds with Lorentzian metrics and analyze Ricci operator eigenvalues.
result Ricci operator has only real eigenvalues for Lorentzian metrics.
Unified plug-in approach for estimating symmetric properties of distributions efficiently.
problem Estimating symmetric properties of distributions with high accuracy and efficiency.
method Profile-maximum-likelihood (PML) based estimator.
result Achieves theoretical limit for universal symmetric property estimation.
The paper examines properties of spherical Finsler metrics, proving their semi-C-reducibility and conditions for vanishing mean stretch curvature.
problem Analyzing curvature properties of spherical Finsler metrics.
method Proving semi-C-reducibility and finding conditions for vanishing mean stretch curvature.
result Conditions for a general spherically symmetric Finsler metric to have vanishing mean stretch curvature.
Extends flat submanifold properties from hyperbolic plane to symmetric spaces.
problem Spectral asymptotics for orbital integrals in symmetric spaces.
method Generalizes geodesic properties to maximal flat submanifolds.
result Establishes geometric properties of maximal flat submanifolds in symmetric spaces.
Study on extended weakly symmetric spaces, classifying and providing an example.
problem Understanding geometric properties of extended weakly symmetric spaces.
method Classification and presentation of a non-trivial example.
result Existence of extended weakly symmetric spaces established.
Study on symmetric automorphisms of RAAGs, proving finiteness properties and contractibility.
problem Finiteness properties and contractibility of symmetric automorphisms of RAAGs.
method Definition of symmetric automorphism group, construction of symmetric Outer space, proof of contractibility.
result Finiteness properties and contractibility results for symmetric automorphisms of RAAGs.
Study differential properties of matrix square roots in specific cases.
problem Understanding matrix square roots in semi-simple, symmetric, and orthogonal cases.
method Analysis of differential and metric structures of real square roots of matrices under specific conditions.
result Differential properties of matrix square roots in semi-simple, symmetric, and orthogonal cases.
Study on Selberg's modified metric in symmetric spaces.
problem Properties of modified metric in symmetric spaces.
method Analysis of SL(n,R)/SO(n,R) with Selberg's premetric. result Generalizations of hyperbolic space properties.
H. A. Hayden [1] introduced the idea of semi-symmetric non-metric connection on a Riemannian manifold in (1932). Agashe and Chafle \cite{1} defined and studied semi-symmetric non-metric connection on a Riemannian manifold. In the present paper, we define a new type of semi-symmetric non-metric connexion in an almost co…
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an especially useful form of the metric of a spherically symmetric spacetime in polar-ar…
Study on symmetric domains with Bergman metric properties.
problem Properties of Bergman metrics in symmetric domains.
method Combining Hermitian symmetric spaces theory, Kähler immersions, and analytic/pluripotential tools.
result Rigidity results for Bergman metrics in bounded domains.
The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric Kenmotsu manifolds with respect to the semi-symmetric non-metric connection.
We find all Ricci semi-symmetric as well as all conformally semi-symmetric spacetimes. Neither of these properties implies the other. We verify that only conformally flat spacetimes can be Ricci semi-symmetric without being conformally semi-symmetric and show that only vacuum spacetimes and spacetimes with just a Λ-t…
We study the differential geometric properties of the manifold of non-singular symmetric real matrices endowed with the trace metric; in case of positive definite matrices we describe the full group of isometries
The paper extends Busemann's inequalities to complex and quaternionic spaces.
problem Extending Busemann's inequalities to complex and quaternionic vector spaces.
method Proof leverages a monotonicity property under symmetrization with respect to complex or quaternionic hyperplanes.
result Standard Steiner symmetrization does not exhibit the monotonicity property in complex or quaternionic spaces.
The Stanley chromatic symmetric function XG of a graph G is a symmetric function generalization of the chromatic polynomial, and has interesting combinatorial properties. We apply the ideas of Khovanov homology to construct a homology of graded Sn-modules, whose graded Frobenius series FrobG(q,t) reduces to …
It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized symmetric spaces.
The Bergman metric on symmetrized bidisc has negative curvature properties.
problem Holomorphic curvature properties of the Bergman metric on symmetrized bidisc.
method Analysis of holomorphic sectional and bisectional curvatures.
result Negative pinched holomorphic sectional curvature and non-positive holomorphic bisectional curvature.
The study characterizes and verifies equivariant embeddings of symmetric Kählerian manifolds.
problem Characterizing and verifying equivariant embeddings of symmetric Kählerian manifolds.
method Investigation motivated by Cartan and Wallach's theorem on symmetric spaces, focusing on CPn and parallel plurimean curvature. result If an equivariant embedding has parallel plurimean curvature, it is the extrinsically symmetric one.
Sharp inequality proven for symmetric functions on a 4D sphere.
problem Proving a sharp Beckner's inequality for axially symmetric functions on S4. method Utilized pointwise properties of Gegenbauer polynomials.
result Sharp Beckner's inequality established for axially symmetric functions on S4. In this paper, a new approach of defining Steiner symmetrization of coercive convex functions is proposed and some fundamental properties of the new Steiner symmetrization are proved. Further, using the new Steiner symmetrization, we give a different approach to prove a functional version of the Blaschke-Santalo inequa…
The paper defines symmetric brackets for skew-symmetric algebroids with totally skew-symmetric torsion.
problem Defining symmetric brackets for skew-symmetric algebroids.
method Using connections with totally skew-symmetric torsion and pseudo-Riemannian metrics.
result Explicit formula for the Levi-Civita connection and symmetric brackets on almost Hermitian manifolds.
The aim of the present paper is to study the properties of Riemannian manifolds equipped with a projective semi-symmetric connection.
Unified method for estimating properties of large domain distributions efficiently.
problem Estimating properties of distributions over large domains efficiently.
method Piecewise-polynomial approximation technique for constructing sample- and time-efficient estimators.
result Near-linear-time computable estimators with optimal and highly-concentrated approximation values.
The study extends kernel universality to Riemannian symmetric spaces.
problem Understanding kernel universality in non-Euclidean domains.
method Harmonic analysis on Riemannian symmetric spaces.
result Proves universality of recent kernels on Riemannian symmetric spaces.
In this work we prove that every locally symmetric smooth submanifold gives rise to a naturally defined smooth submanifold of the space of symmetric matrices, called spectral manifold, consisting of all matrices whose ordered vector of eigenvalues belongs to the locally symmetric manifold. We also present an explicit f…
Study explores associated groups of symmetric quandles and their properties.
problem Understanding the structure and relationships of symmetric quandles and their associated groups.
method Group-theoretic analysis and characterization of associated groups.
result Characterization and properties of associated groups of symmetric quandles.
Study curvature and symplectic properties of symmetric products of surfaces.
problem Distinguishing between macroscopic dimensions in Riemannian manifolds.
method Detailed study of curvature and symplectic properties using symmetric products of surfaces.
result Symmetric products of surfaces sharply distinguish between two macroscopic dimensions.
Study on G2 actions on symmetric spaces, focusing on orbit properties.
problem Investigating properties of orbits in symmetric spaces related to G2. method Classification and analysis of orbits as Riemannian submanifolds, focusing on principal curvatures and specific types of orbits.
result Classification and properties of orbits in symmetric spaces related to G2. The paper studies ∗-η-Ricci-Yamabe solitons on α-Cosymplectic manifolds.
problem Exploring ∗-η-Ricci-Yamabe solitons on α-Cosymplectic manifolds. method Analyzing curvature properties and developing soliton characteristics with respect to quarter-symmetric metric connection.
result Characteristics and nature of ∗-η-Ricci-Yamabe solitons on α-Cosymplectic manifolds. Estimating symmetric properties of a distribution, e.g. support size, coverage, entropy, distance to uniformity, are among the most fundamental problems in algorithmic statistics. While each of these properties have been studied extensively and separate optimal estimators are known for each, in striking recent work, Ac…
Proves symmetric spaces for certain quasi-isometric properties.
problem Understanding quasi-isometric spaces and their properties.
method Analyzes geometric and geometrically finite quasi-actions.
result Proves quasi-isometric spaces are symmetric or real line.
Since the work of Henri Cartan finite dimensional Riemannian symmetric spaces are an important subject of mathematical interest. They are related in a natural way to semisimple Lie groups. In this work we introduce and study their infinite dimensional generalization: Affine Kac-Moody symmetric spaces. Affine Kac-Moody …
We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or anti-symmetrizing pairwise kernel functions. Through spectral analysis, we show that …
Paper classifies compact symmetric triads using double Satake diagrams and canonical forms.
problem Classifying compact symmetric triads.
method Introducing double Satake diagrams and canonical forms, proving their existence and properties.
result Existence and properties of canonical forms for compact simple symmetric triads.
Harmonic functions on compact symmetric spaces exhibit strong convexity properties.
problem Understanding the convexity of harmonic functions on compact symmetric spaces.
method Analyzing the nonnegativity of the Laplacian powers of harmonic functions.
result Harmonic functions on compact symmetric spaces have nonnegative Laplacian powers, demonstrating strong convexity.
This paper aims to provide a better understanding of a symmetric loss. First, we emphasize that using a symmetric loss is advantageous in the balanced error rate (BER) minimization and area under the receiver operating characteristic curve (AUC) maximization from corrupted labels. Second, we prove general theoretical p…
Study attached submanifolds in solvmanifolds, generalizing symmetric space results.
problem Exploring submanifolds in non-symmetric spaces with unusual curvature properties.
method Generalizing Tamaru's construction to pseudo-Riemannian scalar products and root spaces.
result Ricci curvature restriction holds for attached submanifolds under specific algebraic conditions.
In this paper we generalize a result in [1], showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of fixed points of involutions are also proved.
Study on tautness tensor for Riemannian foliations.
problem Understanding tautness properties of Riemannian foliations.
method Investigating a symmetric 2-tensor related to mean curvature.
result Prove a tautness condition for compact manifolds.
Extended symmetric unions extend properties of Alexander polynomials.
problem Properties of Alexander polynomials of symmetric unions.
method Constructing pairs of knots with specific epimorphisms.
result Alexander polynomials of constructed knots exhibit extended properties.
Study geometric properties of SGL submanifolds in a specific manifold.
problem Analyzing geometric characteristics of SGL submanifolds.
method Examines integrability conditions and parallelism properties of distributions.
result Provides insights into geometric behavior of SGL submanifolds.
New infinite-dimensional representations with bounded multiplicity found for Lie groups.
problem Finding representations with bounded multiplicity for Lie groups.
method Proving existence of infinite-dimensional irreducible representations with bounded multiplicity property.
result Infinite-dimensional irreducible representations with bounded multiplicity found for non-compact semisimple Lie groups.
There is a well developed theory of weakly symmetric Riemannian manifolds. Here it is shown that several results in the Riemannian case are also valid for weakly symmetric pseudo-Riemannian manifolds, but some require additional hypotheses. The topics discussed are homogeneity, geodesic completeness, the geodesic orbit…