arXiv subjects
Publications and source records attributed to Santiago López de Medrano.
The goal of this work is to continue the study the smoothings of 3-dimensional manifolds with singularities obtained as small covers of non simple right-angle Coxeter polyhedral orbifolds. They appear in the study of coaxial intersections of ellipsoids. In particular we introduce the concept of $n$-pyramitoid generalizing the $n$-pyramid.
The goal of this work is to study the smoothings of singular coaxial intersections of ellipsoids (where coaxial includes concentric) with generic singularities, with special attention to the 3-dimensional case.
For a family of polytopes of even dimension $2p$, known as \textit{dual-neighborly}, it has been shown for $p\ne 2$ that the associated intersection of quadrics is a connected sum of sphere products $S^p\times S^p$. In this article we give formulas for the number of terms in that connected sum. Certain combinatorial operations produce new polytopes whose associated intersections are also connected sums of sphere products and we give also formulas for their number. These include a large amount of simple polytopes, including many odd-dimensional ones.
We construct open book structures on all moment-angle manifolds and describe the topology of their leaves and bindings under certain restrictions. II. We also show, using a recent deep result about contact forms due to Borman, Eliashberg and Murphy [6], that every odd-dimensional moment-angle manifold admits a contact structure. This contrasts with the fact that, except for a few, well-determined cases, even-dimensional ones do not admit symplectic structures. We obtain the same results for large families of more general intersections of quadrics.
We show that the mutants of compactified representations constructed by Franz and Puppe can be written as intersections of real quadrics involving division algebras and as generalizations of polygon spaces. We also show that these manifolds are connected sums of products of spheres.
We construct open book structures on moment-angle manifolds and give a new construction of examples of contact manifolds in arbitrarily large dimensions.
Schwartz's solution to the Björling problem leads to an equivalence class of spatial strips S(t)=(c(t),n(t)) which produce equivalent minimal surfaces. For the particular case when the generating strip S(t) belongs to some plane E and c(t) is symmetric with respect to some straight line in E, the symmetries of the minimal surface permit us to identify another planar curve ~c(t) that we call the CPG curve to c(t). A simple symmetric argument shows that self-CPG curves produce minimal surfaces whose adjoint surface contains another self-CPG curve. We ask for minimal surfaces generated by self-CPG curves which are self-adjoints.
We give a parameterization of Alfred Gray's Elliptical Catenoid and Elliptical Hellicoid using Jacobi's elliptic functions. This parameterization avoids some problems present in the original depiction of these surfaces.