Condition for symmetric 3-differentials on complex surfaces.
problem Conditions for representing symmetric 3-differentials as products of holomorphic forms.
method Two coordinate versions of a necessary and sufficient condition.
result Locally representable symmetric 3-differentials as products of holomorphic forms.
Paper extends previous result on hypersurfaces with degenerate light-like points.
problem Characterizing hypersurfaces with degenerate light-like points in Lorentzian manifolds.
method Analyzes C3-differentiable hypersurfaces, extending previous C4-differentiability result. result Same conclusion holds for C3-differentiable hypersurfaces as for C4-differentiable ones. Study on affine surfaces with specific algebraic properties.
problem Characterize homogeneous affine surfaces with Hessian rank 2.
method Investigate algebra of differential invariants under affine transformation group.
result Organize homogeneous models into inequivalent branches.
We define a nondegenerate Monge-Ampère structure on a 6-dimensional manifold as a pair (Ω,ω), such that Ω is a symplectic form and ω is a 3-differential form which satisfies ω∧Ω=0 and which is nondegenerate in the sense of Hitchin. We associate with such a pair a generalized almost (pseudo) Calabi-Yau stru…
We define a non-degenerated Monge-Ampere structure on a 6-manifold associated with a Monge-Ampere equation as a couple (Ω,ω), such that Ωis a symplectic form and ωis a 3-differential form which satisfies ω\wedgeΩ=0 and which is non-degenerated in the sense of Hitchin. We associate with such a couple an almost (pseudo) …
A Riemann-Cartan manifold is a Riemannian manifold endowed with an affine connection which is compatible with the metric tensor. This affine connection is not necessarily torsion free. Under the assumption that the manifold is a homogeneous space, the notion of homogeneous Riemann-Cartan space is introduced in a natura…
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 paper classifies symmetric triads with multiplicities and their applications.
problem Classifying symmetric triads with multiplicities and their applications.
method Developed the theory of symmetric triads with multiplicities, classified abstract triads, and determined corresponding triads for commutative compact triads.
result Classified symmetric triads with multiplicities and their applications.
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 establish a new symmetrization procedure for the isoperimetric problem in symmetric spaces of noncompact type. This symmetrization generalizes the well known Steiner symmetrization in euclidean space. In contrast to the classical construction the symmetrized domain is obtained by solving a nonlinear elliptic equatio…
Study on totally symmetric sets with group applications.
problem Understanding totally symmetric sets and their group applications.
method Survey of existing theory and applications to various groups.
result Exploration of totally symmetric sets in multiple group contexts.
In this article, we summarize the results on symmetric conformal geometries. We review the results following from the general theory of symmetric parabolic geometries and prove several new results for symmetric conformal geometries. In particular, we show that each symmetric conformal geometry is either locally flat or…
Study properties of Kenmotsu manifolds with a specific connection.
problem Properties of Kenmotsu manifolds with a semi-symmetric non-metric connection.
method Analysis of generalized recurrent, Ricci-recurrent, weakly symmetric, and weakly Ricci-symmetric properties.
result New findings on properties of Kenmotsu manifolds under semi-symmetric non-metric connection.
Study on special manifolds with specific connections.
problem Characterizing locally φ-symmetric LP-Sasakian manifolds with semi-symmetric metric connection.
method Analyzing properties of locally φ-symmetric LP-Sasakian manifolds with semi-symmetric metric connection.
result Necessary and sufficient condition for local φ-symmetry with Levi-Civita connection.
New method answers open question on symmetric diagrams.
problem Symmetric equivalence of symmetric union diagrams.
method Refined topological spin models.
result Complete answer to open question.
Symmetric Poisson structures linked to geodesic foliations and Jordan algebras.
problem Understanding geometric structures related to geodesic foliations and dynamics.
method Introducing symmetric Poisson structures, proving correspondences with geodesic foliations and Jordan algebras.
result Symmetric Poisson structures correspond to totally geodesic foliations and Jacobi-Jordan algebras.
Complete classification of quaternionic skew-Hermitian symmetric spaces found.
problem Classifying quaternionic skew-Hermitian symmetric spaces.
method Proving the existence of a torsion-free mSO∗(2n)mSp(1)-structure and showing that any homogeneous space is symmetric. result A complete classification of quaternionic skew-Hermitian symmetric spaces for arbitrary n>1. The paper defines left-symmetric bialgebroids and their Manin triples.
problem No specific problem stated; focuses on definitions and constructions.
method Introduced left-symmetric bialgebroids and Manin triples, constructed from pseudo-Hessian manifolds.
result Established a relation between Maurer-Cartan type equations and Dirac structures.
Symmetric quandles provide new insights into link colorings.
problem Understanding link colorings using quandles.
method Construction of symmetric quandles and isomorphism of their cohomology groups.
result Homology groups of quandles are isomorphic to those of their symmetric doubles.
The paper explores symmetric losses for better learning from corrupted labels.
problem Learning from corrupted labels with balanced error rate or AUC maximization.
method Proves theoretical properties of symmetric losses and proposes a convex barrier hinge loss.
result Symmetric losses are advantageous in BER minimization and AUC maximization from corrupted labels.
Study para-Sasakian φ-symmetric spaces using Boothby-Wang fibration.
problem Characterize para-Sasakian φ-symmetric spaces.
method Use Boothby-Wang fibration to construct and provide examples.
result Explicit construction and example of para-Sasakian φ-symmetric spaces.
New (co)homology theory for symmetric quandles developed.
problem Developing strong invariants for symmetric quandles.
method Introducing symmetric quandle modules and Beck modules, extending module theory, and constructing generalized (co)homology.
result Established an explicit isomorphism between symmetric quandle cohomology and group cohomology.
Discusses existence of specific types of symmetric manifolds.
problem Existence of weakly cyclic Z-symmetric manifolds. method Analyzes defining conditions and provides examples.
result Provides proper examples of weakly cyclic Z-symmetric manifolds. Formulae for non-symmetric connections derived from covariant derivatives.
problem Deriving commutation formulae for non-symmetric affine connections.
method Covariant derivatives of tensors with respect to symmetric and non-symmetric affine connections.
result Formulae for non-symmetric connections derived from covariant derivatives.
Paper introduces capillary Schwarz symmetrization in half-space.
problem Capillary problems in half-space.
method Introduces a special anisotropic gauge to transform capillary symmetrization to convex symmetrization.
result Capillary Schwarz symmetrization in half-space established.
New proof for symmetric spaces with rectangular lattices.
problem Characterizing symmetric spaces with rectangular unit lattices.
method Explicit construction of isometric embeddings and analysis of root systems.
result Symmetric spaces with rectangular unit lattices are symmetric R-spaces.
Develops symmetric Cartan calculus linking to Patterson-Walker metric.
problem No specific problem stated; focuses on developing a new calculus.
method Symmetric Cartan calculus, using torsion-free affine connections.
result Symmetric Cartan calculus is a complete analogue of classical Cartan calculus.
We construct and identify star representations canonically associated with holonomy reducible simple symplectic symmetric spaces. This leads the a non-commutative geometric realization of the correspondence between causal symmetric spaces of Cayley type and Hermitian symmetric spaces of tube type.
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.
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 …
Defines semi-symmetric metric connection on super warped products.
problem Computing curvature and Ricci tensors on super warped products.
method Introduced semi-symmetric metric connection and conditions for Einstein spaces.
result Conditions for super warped product spaces to be Einstein with semi-symmetric metric connection.
Classifies totally geodesic submanifolds in symmetric spaces.
problem Classifying submanifolds in symmetric spaces.
method Classification of totally geodesic submanifolds in products of rank one symmetric spaces.
result Infinitely many examples of irreducible totally geodesic submanifolds in Hermitian symmetric spaces.
Study on submanifolds of Euclidean space, classifying their symmetry types.
problem Classifying symmetry types of submanifolds in Euclidean space.
method Analyzing properties of full irreducible almost symmetric submanifolds and their cohomogeneity.
result Classification of almost symmetric submanifolds into specific types.
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.
Locally 2-fold symmetric manifolds are proven to be locally symmetric.
problem Characterizing and proving symmetry properties of manifolds.
method Definition and analysis of locally k-fold symmetric manifolds, application of local isometries.
result Locally 2-fold symmetric manifolds are shown to be locally symmetric.
We provide a simple proof that conformally semi-symmetric spacetimes are actually semi-symmetric. We also present a complete refined classification of the semi-symmetric spacetimes.
Classifies maximal antipodal sets in symmetric spaces.
problem Identifying maximal antipodal sets in symmetric spaces.
method Explicit classification for most irreducible compact symmetric spaces.
result Classification of maximal antipodal sets in most symmetric spaces.
Paper proves eigenvalue inequality for Hopf-symmetric domains.
problem Eigenvalue inequality for Hopf-symmetric domains in non-compact symmetric spaces.
method Used geometric and spectral analysis on non-compact rank one symmetric spaces.
result Eigenvalue inequality for bounded Hopf-symmetric domains in non-compact symmetric spaces.
The paper classifies Landsberg spherically symmetric Finsler metrics in various dimensions.
problem Investigating compatibility conditions on spherically symmetric Finsler metrics.
method Using the inverse problem of calculus of variations, the paper focuses on Landsberg and Berwald types.
result All Landsberg spherically symmetric manifolds in higher dimensions are either Riemannian or have specific geodesic spray formulas.
Classification extended for reducible symmetric spaces.
problem Classifying homogeneous foliations on symmetric spaces.
method Extended classification from irreducible to reducible symmetric spaces.
result Classification completed for all noncompact symmetric spaces.
Survey on systole growth in congruence symmetric spaces.
problem Understanding systole growth in congruence symmetric spaces.
method Survey and simple proofs for best constants.
result Best possible constants for systole growth in symmetric spaces.
Bounded symmetric domains are biholomorphic to tube domains over Finsler symmetric cones.
problem Characterizing biholomorphic mappings between tube domains and bounded symmetric domains.
method Analyzing properties of Finsler symmetric cones and unital JB-algebras.
result Tube domains over Finsler symmetric cones are biholomorphic to bounded symmetric domains.
Defines Jacobi-Koszul-Vinberg structures on Jacobi-left-symmetric algebroids.
problem No specific problem stated; focuses on new structure definition.
method Definition and properties of Jacobi-Koszul-Vinberg structures on Jacobi-left-symmetric algebroids.
result Defines a new structure on Jacobi-left-symmetric algebroids.
In this paper, we introduce a notion of a left-symmetric algebroid, which is a generalization of a left-symmetric algebra from a vector space to a vector bundle. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie algebroid. We construct left-symmetric algebroids from $\mathcal …
Study finds all 4D homogeneous semi-symmetric Lorentzian manifolds.
problem Characterizing semi-symmetric Lorentzian manifolds.
method Used algebraic curvature tensors to determine all 4D manifolds.
result Found all four-dimensional homogeneous semi-symmetric Lorentzian manifolds.
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.
Study constructs Frenet curves using semi-symmetric metric connection.
problem Understanding Frenet curves in various manifolds.
method Using semi-symmetric metric connection to construct Frenet frames and curvatures.
result Examples of semi-symmetric Frenet curves in Euclidean, Sasakian, and Kenmotsu manifolds.
Axel Seeliger tabulated ribbon knots and found non-symmetric examples.
problem Identifying non-symmetric ribbon knots.
method Tabulated symmetric union presentations and band diagrams for ribbon knots.
result Found non-symmetric ribbon knots with 11 and 12 crossings.