Annali di Matematica Pura ed Applicata最新文献

We investigate isometric immersions (f:M^nrightarrow mathbb {R}^{n+2}), (nge 3), of Riemannian manifolds into Euclidean space with codimension two that admit isometric deformations that preserve the metric of the Gauss map. In precise terms, the preservation of the third fundamental form of the submanifold must be ensured throughout the deformation. For minimal isometric deformations of minimal submanifolds this is always the case. Our main result is of a local nature and states that if f is neither minimal nor reducible, then it is a hypersurface of an isometrically deformable hypersurface (F:tilde{M}^{n+1}rightarrow mathbb {R}^{n+2}) such that the deformations of F induce those of f. Moreover, for a particular class of such submanifolds, a complete local parametric description is provided.

In this paper we prove that any full Perazzo algebra (A_F), whose Macaulay dual generator is a Perazzo form (Fin K[X_0,dots ,X_n,U_1,dots ,U_m]_d) with (n+1 = left( {begin{array}{c}d+m-2 m-1end{array}}right) ), is the doubling of a 0-dimensional scheme in (mathbb {P}^{n+m}) and we compute the graded Betti numbers of a minimal free resolution of (A_F).

We give the algebraic and topological description of the moduli spaces of flat metrics for the 4-dimensional closed flat manifolds with two or three generators in their holonomy, which completes the analysis made in García (Differ Geom Appl 88:101996-18, 2023).

In this paper, we introduce a geometric description of contact Lagrangian and Hamiltonian systems on Lie algebroids in the framework of contact geometry, using the theory of prolongations. We discuss the relation between Lagrangian and Hamiltonian settings through a convenient notion of Legendre transformation. We also discuss the Hamilton-Jacobi problem in this framework and introduce the notion of a Legendrian Lie subalgebroid of a contact Lie algebroid.

In this article we present the existence of infinitely many non-radial positive or sign-changing solutions for the following FitzHugh–Nagumosystem:

where (Nge 5), (delta >0), (g(u)=(a_0+1)u^2-u^3), (0<a_0<frac{1}{2}) and (a(|x|)in (0,frac{1}{2})) satisfies some decay conditions at the infinity. More precisely, for any positive integer k large, there is a (delta _k>0) such that for (0<delta <delta _k), there exists positive solutions with 2k peaks, which are respectively concentrated at the vertices of a regular k-polygon on two circles in 3-dimensional space with the radium (rsim k ln k) and the height (hsim frac{1}{k}). In addition, the sign-changing solutions with 2k peaks are evenly distributed on the equatorial (textrm{T}={xin mathbb {R}^2:x_1^2+x_2^2=r^2}) in the ((x_1, x_2))-plane. As a by-product, we give the similar results of Schödinger-Poisson in (mathbb {R}^N) for (Nge 3).

Rhaly operators, as generalizations of the Cesàro operator, are studied from the standpoint of view of spectral theory and invariant subspaces, extending previous results by Rhaly and Leibowitz to a framework where generalized Cesàro operators arise naturally.

We obtain the list of automorphism groups for smooth plane sextic curves over an algebraically closed field K of characteristic (p=0) or (p>21). Moreover, we assign to each group a geometrically complete family over K that describe the corresponding stratum, that is, a generic polynomial equation with parameters such that any curve in the stratum is K-isomorphic to a smooth plane model obtained by specializing the values of those parameters in K. Additionally, we explore the connection with K3 surfaces of degree 2.

We present efficient classification algorithms for log del Pezzo surfaces with torus action of Picard number one and given Gorenstein index. Explicit results are obtained up to Gorenstein index 200.

Generalizing the Martens theorem for line bundles over a curve C, we obtain upper bounds on the dimension of the Brill–Noether locus (B^k_{n, d}) parametrizing stable bundles of rank (n ge 2) and degree d over C with at least k independent sections. This proves a conjecture of the second author and generalizes bounds obtained by him in the rank two case. We give more refined results for some values of d, including a generalized Mumford theorem for (n ge 2) when (d le g - 1). The statements are obtained chiefly by analysis of the tangent spaces of (B^k_{n, d}). As an application, we show that for (nge 5) the locus (B^2_{n, n(g-1)}) is irreducible and reduced for any C.