相关论文: An estimate for the Singer invariant via the Jet I…
The Singer algebraic transfer is a fundamental homomorphism in algebraic topology, providing a bridge between the homology of classifying spaces and the cohomology of the Steenrod algebra $\mathcal{A}$, which forms the $E_2$-term of the…
Ray Singer torsion is a numerical invariant associated with a compact Riemannian manifold equipped with a flat bundle and a Hermitian structure on this bundle. In this note we show how one can remove the dependence on the Riemannian metric…
We prove the Singer conjecture for varieties with semismall Albanese map and residually finite fundamental group.
We present a systematic, algorithmic method to compute the preimage of elements under the Singer algebraic transfer. Using the lambda algebra and the invariant-theoretic formula of P.H. Chon and L.M. Ha [5], we formulate the preimage search…
In this paper, we compute Riemannian metrics on the Siegel-Jacobi space which are invariant under the natural action of the Jacobi group explicitly and also provide the Laplacians of these invariant metrics. These are expressed in terms of…
Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner…
A classical theorem of Riemannian geometry, due in its original form to Cartan, states that the Taylor expansion of the metric in geodesic normal coordinates is a universal formal power series involving only the symmetrizations of the…
In this paper we construct the jet geometrical extensions of the KCC-invariants, which characterize a given second-order system of differential equations on the 1-jet space $J^1(R,M)$. A generalized theorem of characterization of our jet…
We express invariants of Finsler manifolds in a geometrical way by means of using moving planes and their associated Jacobi curves, which are curves in a fixed homogeneous Grassmann manifold. Some applications are given.
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…
In this paper, we study Jacobi operators associated to algebraic curvature maps (tensors) on lightlike submanifolds M. We investigate conditions for an induced Rie- mann curvature tensor to be an algebraic curvature tensor on M. We…
The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian…
Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the…
This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator $T$ on a Hilbert space with an orthogonal basis, we define the isomorphic structure $\Sigma(T)$ as the family of all subsets…
The main result of this article provides a characterization of reductive homogeneous spaces equipped with some geometric structure (non necessarily pseudo-Riemannian) in terms of the existence of certain connection. The result generalizes…
We give practical numerical methods to compute the period matrix of a plane algebraic curve (not necessarily smooth). We show how automorphisms and isomorphisms of such curves, as well as the decomposition of their Jacobians up to isogeny,…
Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…
We use the density function of a harmonic space to obtain estimates for the eigenvalues of the Jacobi operator; when these estimates are sharp, then the harmonic space is a symmetric Osserman space.
We characterize isometric actions whose principal orbits are hypersurfaces through the existence of a linear connection satisfying a set of covariant equations in the same spirit as the Ambrose-Singer Theorem for homogeneous space. These…
We study meromorphic jacobian pairs, i.e., pairs of polynomials in one variable, with coefficients meromorphic series in a second variable, whose jacobian relative to the two variables depends only on the second variable. We pose two…