arXiv research

Paper offers a framework for estimating symmetric properties efficiently.

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.

Study properties of semi-symmetric Lorentzian spaces, foliated manifolds.

Unified plug-in approach for estimating symmetric properties of distributions efficiently.

The paper examines properties of spherical Finsler metrics, proving their semi-C-reducibility and conditions for vanishing mean stretch curvature.

Extends flat submanifold properties from hyperbolic plane to symmetric spaces.

Study on extended weakly symmetric spaces, classifying and providing an example.

Study on symmetric automorphisms of RAAGs, proving finiteness properties and contractibility.

Study differential properties of matrix square roots in specific cases.

Study on Selberg's modified metric in symmetric spaces.

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…

The aim of the present paper is to study the properties of Kenmotsu manifolds equipped with a non-symmetric non-metric connection. We also establish some curvature properties of Kenmotsu manifolds. It is proved that a Kenmotsu manifold endowed with a non-symmetric non-metric is irregular.

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.

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.

The Stanley chromatic symmetric function $X_G$ 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 $S_n$-modules, whose graded Frobenius series $Frob_G(q,t)$ 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.

We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and time-efficient estimators for all sufficiently smooth, symmetric and non-symmetric, …

The study characterizes and verifies equivariant embeddings of symmetric Kählerian manifolds.

Sharp inequality proven for symmetric functions on a 4D sphere.

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…

In this note, we discuss symmetric brackets on skew-symmetric algebroids associated with a metric structure. Given a pseudo-Riemannian metric structure, we describe symmetric brackets induced by connections with totally skew-symmetric torsion in the language of Lie derivatives and differentials of functions. In particu…

The aim of the present paper is to study the properties of Riemannian manifolds equipped with a projective semi-symmetric connection.

The study extends kernel universality to 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.

Study curvature and symplectic properties of symmetric products of surfaces.

Study on $G_{2}$ actions on symmetric spaces, focusing on orbit properties.

The paper studies $*$-$η$-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.

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.

Harmonic functions on compact symmetric spaces exhibit strong convexity properties.

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.

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.

Extended symmetric unions extend properties of Alexander polynomials.

New infinite-dimensional representations with bounded multiplicity found for Lie groups.

Study geometric properties of SGL submanifolds in a specific manifold.

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…