arXiv research

Study on 3D Lie groups' symmetry index, proving positive index for all.

Study finds index of symmetry for solvable 3D Lie groups with left-invariant metrics.

New tools compute index of symmetry in homogeneous fibrations.

Study on symmetric operators on non-compact manifolds, focusing on their index modulo 2.

We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive spaces. In this case, the so-called leaf of symmetry turns out to be of the group type…

Study of symmetries in 3D Lie groups, determining index and moduli space properties.

We study the index of symmetry of a compact generalized flag manifold M=G/H endowed with an invariant Kaehler structure. When the group G is simple we show that the leaves of symmetry are irreducible Hermitian symmetric spaces and we estimate their dimension.

We develop a general structure theory for compact homogeneous Riemannian manifolds in relation to the co-index of symmetry. We will then use these results to classify irreducible, simply connected, compact homogeneous Riemannian manifolds whose co-index of symmetry is less or equal than three. We will also construct ma…

Study on metrics on specific nilmanifolds, finding new examples and properties.

The paper identifies and constructs metrics for specific homogeneous spaces.

We find flat band Hamiltonians and Ginsparg-Wilson relations for symmetry classes.

Massive fermions help understand index theorems without chiral symmetry.

Refined 3D index uses surgery and gradings to distinguish 3-manifolds.

New method uses spherical harmonics to simplify learning single-index models.

Finite index solutions to Bernoulli problem are always axially symmetric.

The study explores Hesse manifolds and their symmetries in multifield cosmological models.

Testing symmetry of a probability distribution is a common question arising from applications in several fields. Particularly, in the study of observables used in the analysis of stock market index variations, the question of symmetry has not been fully investigated by means of statistical procedures. In this work a di…

The paper connects flatness to generalization in learning multi-index models with neural networks.

We study the Kaehler metric given by the logarithm of a cubic form on its complexified index cone. Under mirror symmetry, this metric should asymptotically correspond to the Weil-Petersson metric. Using the theory of special Kaehler manifolds, a proof of a curvature formula for this metric is given.

Geometrically describes parity anomaly in fermionic systems.

Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2,2) gauge transformations acting on the spinor index of the wave functions. This local U(2,2) symmetry allows a unified description of electrodynamics and genera…

Study of spectral flow in symmetric Toeplitz operator families.

Study on Hitchin index for cohomogeneity one nearly Kähler structures.

Formula for Z_2-valued index of symmetric operators on manifolds.

Employing data on the assessed value of land in 1983 -- 2005 Japan, we investigate the dynamical behavior in the high scale region of non-equilibrium systems. From the detailed quasi-balance and Gibrat's law, we derive a relation between the change of Pareto index and a symmetry in the detailed quasi-balance. The relat…

The study explores the symmetries of exotic negatively curved manifolds.

Study of MHD equilibria with orientation-reversing symmetry, showing all orbits are periodic.

Existence of an infinite sequence of harmonic maps between spheres of certain dimensions was proven by Bizon and Chmaj. This sequence shares many features of the Bartnik-McKinnon sequence of solutions to the Einstein-Yang-Mills equations as well as sequences of solutions that have arisen in other physical models. We ap…

Paper introduces Lie algebroid index theory and a generalized Riemann-Roch theorem.

Unique genus 2 minimal surface in S^3 with specific symmetry group.

Estimates complex models without assuming Gaussian symmetry, achieving near-optimal performance.

Paper solves curvature prescription on unit ball with sign-changing functions.

Unified geometric perspectives on PDEs, torsion invariants, and moduli theory.

Proves transversality for local Morse homology with symmetries.

Study on submanifolds of Euclidean space, classifying their symmetry types.

Symmetry analysis of financial trends returns reveals bi-modality and multi-scale behavior.

Physicists explain a mathematical theorem about topological insulators.

Study uncovers complex critical points in tensor decomposition.

The paper calculates critical points of systole function on Teichmüller space.

We show that if $g$ is a Riemannian metric on a closed piecewise locally symmetric manifold $M$, then the lift of $g$ to the universal cover $\widetilde{M}$ has a discrete isometry group. We also show that the index $[\Isom(\widetilde{M}): π_1(M)]$ is bounded by a constant independent of $g$.

We investigate the dynamical behavior in the large scale region of non-equilibrium systems, by employing data on the assessed value of land in 1983 -- 2006 Japan. In the system we find the detailed quasi-balance, which has the symmetry: x_1 -> a {x_2}^θ (x_1 and x_2 are two successive land prices). By using the detaile…

We select the $n$ stocks traded in the New York Stock Exchange and we form a statistical ensemble of daily stock returns for each of the $k$ trading days of our database from the stock price time series. We study the ensemble return distribution for each trading day and we find that the symmetry properties of the ensem…

We consider generators of algebraic curvature tensors R which can be constructed by a Young symmetrization of product tensors U*w or w*U, where U and w are covariant tensors of order 3 and 1. We assume that U belongs to a class of the infinite set S of irreducible symmetry classes characterized by the partition (2,1). …

New spectral estimates for minimal surfaces with boundary conditions.

We construct and analyze minimal disc stackings with bounds on their Morse index.

Mathematical proof of index equality for lattice Dirac operators and continuum operators.

Rigidity theorem for critical points of Allen-Cahn equation on S³.

Let P be the right-angled dodecahedron or 120-cell in hyperbolic space, and let W be the group generated by reflections across codimension-one faces of P. We prove that if Gamma is a torsion-free subgroup of minimal index in W, then the corresponding hyperbolic manifold H^n/Gamma is determined up to homeomorphism by Ga…