arXiv subjects

Josué Meléndez

Publications and source records attributed to Josué Meléndez.

3 recordsLinked to original sources

arXiv2026

Geometric Properties and Spectral Estimates on Warped Products

We establish an integral inequality for the Ricci curvature of a certain class of warped products $M\times_fN$, where the equality holds if and only if it is simply a Riemannian product. We also give a sufficient condition for the intersection of a warped product $M=\mathbb{R}\times_fP$ with a totally geodesic hypersurface $N$ in an arbitrary Riemannian space to be a totally geodesic slice of $M$. In addition, we establish some spectral estimates for the Laplacian of a submanifold $N$ that intersects a warped product in the same ambient manifold.

math.DG↗

arXiv2019

On the sectional curvature along central configurations

In this paper we characterize planar central configurations in terms of a sectional curvature value of the Jacobi-Maupertuis metric. This characterization works for the $N$-body problem with general masses and any $1/r^α$ potential with $α> 0$. We also observe dynamical consequences of these curvature values for relative equilibrium solutions. These curvature methods work well for strong forces ($α\ge 2$).

math.DG↗

arXiv2016

Hyperbolic Shirts fit a 4-body Problem

Consider the equal mass planar $4$-body problem with a potential corresponding to an inverse \textit{cube} force. The Jacobi-Maupertuis principle reparametrizes the dynamics as geodesics of a certain metric. We examine the curvature of this geodesic flow in the reduced space on the collinear and parallelogram invariant surfaces and derive some dynamical consequences. This proves a numerical conjecture of [4].

math.DS↗