arXiv research

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…

Proves conditions for Fourier transforms in rank 1 symmetric spaces.

Defines strongest integrability condition for skew-symmetric endomorphisms.

The study finds conditions for quaternionic structures on symmetric spaces.

Characterizes spherical Finsler metrics satisfying a specific condition.

Study on tautness tensor for Riemannian foliations.

Theory of symmetric rigidity in hyperbolic geometry.

The paper studies T-tensor of spherically symmetric Finsler metrics and characterizes metrics satisfying the T-condition.

Symmetric Poisson structures linked to geodesic foliations and Jordan algebras.

The object of the present paper is to study locally $φ$-symmetric LP-Sasakian manifolds admitting semi-symmetric metric connection and obtain a necessary and sufficient condition for a locally $φ$-symmetric LP-Sasakian manifold with respect to semi-symmetric metric connection to be locally $φ$-symmetric LP-Sasakian man…

The object of this paper is to obtain the concircular curvature tensor of the semi symmetric non-metric connection on the Weyl manifold and to give a necessary and sufficient condition for a semi symmetric non-metric connection to be S-concircular.

The paper explores symmetric representations of links and conditions for amphichirality.

The paper classifies Landsberg spherically symmetric Finsler metrics in various dimensions.

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

The study examines conditions for symmetric and alternating subgroups in mapping class groups of surfaces.

The paper studies a new connection on Riemannian manifolds and finds conditions for symplectic manifolds.

In this paper we study curvature properties of semi-symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,\widetilde g)$ of a Kähler-Norden manifold $(\overline M,\overline J,\overline g,\overline {\widetilde g})$ of constant totally real sectional curvatures $\overline ν$ and …

This paper explores Lorentzian manifolds with specific connections and their symmetries.

We derive a necessary and sufficient condition for the existence of symmetric space structures on quotients of Banach symmetric spaces. Along the way, we investigate the different kinds of reflection subspaces and their Lie triple systems.

Extends Calabi operator to Riemannian locally symmetric spaces.

DPW method reconstructs minimal and symmetric CMC surfaces in 3-sphere.

Connections with (skew-symmetric) torsion on non-symmetric Riemannian manifold satisfying the Einstein metricity condition (NGT with torsion) are considered. It is shown that an almost Hermitian manifold is an NGT with torsion if and only if it is a Nearly Kähler manifold. In the case of an almost contact metric manifo…

New algorithms learn simple staged trees from data, improving model fit.

The object of the present note is to discuss about the defining condition of weakly cyclic Ricci symmetric manifolds and weakly cyclic $Z$-symmetric manifolds \cite{DMS15} and the existence of such notion by proper examples.

The paper defines conditions for good involutions in generalized Alexander quandles.

In this paper, we study eigenvalues and eigenfunctions of $p$-Laplacians with Dirichlet boundary condition on graphs. We characterize the first eigenfunction (and the maximum eigenfunction for a bipartite graph) via the sign condition. By the uniqueness of the first eigenfunction of $p$-Laplacian, as $p\to 1,$ we ident…

Bounded symmetric domains are biholomorphic to tube domains over Finsler symmetric cones.

Bayesian networks are simplified for categorical variables using staged trees and asymmetry-labeled DAGs.

Paper finds obstructions to compact Clifford-Klein forms for tangential symmetric spaces.

Defines semi-symmetric metric connection on super warped products.

In this paper, we prove that full irreducible curvature-adapted isoparametric submanifolds of codimension greater than one in a symmetric space of non-compact type are principal orbits of Hermann actions on the symmetric spaces under certain conditions.

The paper consider the symmetric of Finsler spaces. We give some conditions about globally symmetric Finsler spaces. Then we prove that these spaces can be written as a coset space of Lie group with an invariant Finsler metric. Finally, we prove that such a space must be Berwaldian

The paper characterizes spherically symmetric metrics with scalar curvature.

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an important class of harmonic maps into symmetric and $k$-symmetric spaces. In parti…

Study attached submanifolds in solvmanifolds, generalizing symmetric space results.

We show that a totally geodesic submanifold of a symmetric space satisfying certain conditions admits an extension to a minimal submanifold of dimension one higher, and we apply this result to construct new examples of complete embedded minimal submanifolds in simply connected noncompact globally symmetric spaces.

Investigates locally symmetric polynomial metrics in Riemannian and Finslerian surfaces.

Symmetric losses improve classifier robustness from corrupted labels.

In the literature, there are two different notions of pseudosymmetric manifolds, one by Chaki [7] and other by Deszcz [16], and there are many papers related to these notions. The object of the present paper is to deduce necessary and sufficient conditions for a Chaki pseudosymmetric [7] (resp. pseudo Ricci symmetric […

Generalizes Riemann's results on flat coordinates for non-symmetric bilinear forms.

We study the exponential map of connected symmetric spaces and characterize, in terms of midpoints and of infinitesimal conditions, when it is a diffeomorphism, generalizing the Dixmier-Saito theorem for solvable Lie groups. We then give a geometric characterization of the (strongly) exponential solvable symmetric spac…

Uniformizes klt pairs using bounded symmetric domains.

Paper refines Talagrand inequality on Euclidean spaces.

In this note we discuss conditions under which a linear connection on a manifold equipped with both a symmetric (Riemannian) and a skew-symmetric (almost-symplectic or Poisson) tensor field will preserve both structures.

Study geodesic flow on symmetric surfaces to determine parabolic type.

The paper studies special warped products with a specific connection on super Riemannian manifolds.

Paper proves March's criterion for transience on symmetric manifolds.

Study on Einstein warped spaces with specific connections and curvature properties.