Related papers: Osculating behavior of Kummer surface in $\mathbb …

A generalized Kummer surface $X=Km_{3}(A,G_{A})$ is the minimal resolution of the quotient of a $2$-dimensional complex torus by an order 3 symplectic automorphism group $G_{A}$. A Kummer structure on $X$ is an isomorphism class of pairs…

We determine which connected surfaces can be partitioned into topological circles. There are exactly seven such surfaces up to homeomorphism: those of finite type, of Euler characteristic zero, and with compact boundary components. As a…

Surfaces admitting flows all whose orbits are dense are called minimal. Minimal orientable surfaces were characterized by J.C. Beni\`{e}re in 1998, leaving open the nonorientable case. This paper fills this gap providing a characterization…

We consider the asymptotic behavior of properly embedded minimal surfaces in the product of the hyperbolic plane with the line, taking into account the fact that there is more than one natural compactification of this space. This provides a…

The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…

We define the quantile set of order $\alpha \in \left[ 1/2,1\right) $ associated to a law $P$ on $\mathbb{R}^{d}$ to be the collection of its directional quantiles seen from an observer $O\in \mathbb{R}^{d}$. Under minimal assumptions these…

Cancellative dimer algebras on a torus have many nice algebraic and homological properties. However, these nice properties disappear for dimer algebras on higher genus surfaces. We consider a new class of quiver algebras on surfaces, called…

We classify real hypersurfaces with isometric Reeb flow in the complex quadrics Q^m for m > 2. We show that m is even, say m = 2k, and any such hypersurface is an open part of a tube around a k-dimensional complex projective space CP^k…

Let $M$ be a compact 3-manifold with a triangulation $\tau$. We give an inequality relating the Euler characteristic of a surface $F$ normally embedded in $M$ with the number of normal quadrilaterals in $F$. This gives a relation between a…

Fix an integer $d>0$. In 2008, David and Weston showed that, on average, an elliptic curve over $\mathbf{Q}$ picks up a nontrivial $p$-torsion point defined over a finite extension $K$ of the $p$-adics of degree at most $d$ for only…

We show that the method of moving quadrics for implicitizing surfaces in P^3 applies in certain cases where base points are present. However, if the ideal defined by the parametrization is saturated, then this method rarely applies.…

This paper, which is an outgrowth of a previous paper of the authors, continues the study of dimension 1 foliations on non-metrisable manifolds emphasising some anomalous behaviours. We exhibit surfaces with various extra properties like…

We determine normal forms for the Kummer surfaces associated with abelian surfaces of polarization of type $(1,1)$, $(1,2)$, $(2,2)$, $(2,4)$, and $(1,4)$. Explicit formulas for coordinates and moduli parameters in terms of Theta functions…

If the cyclic sequence of faces for all the vertices in a map are of same type, then the map is said to be a semi-equivelar map. In this article, we classify all the types of semi-equivelar maps on the surface of Euler genus 3, $i.e.$, on…

Kollar and Ruan proved symplectic deformation invariance for uniruledness of Kaehler manifolds. Zhiyu Tian proved the same for rational connectedness in dimension < 4. Kollar conjectured this in all dimensions. We prove Kollar's conjecture,…

We have generalized the Edwards' method of collective description of dense polymer systems in terms of effective potentials to polymer blends in the presence of a surface. With this method we have studied conformationally asymmetric…

If $\alpha\in\r$, an $\alpha$-stationary surface in Euclidean space is a surface $\Sigma$ whose mean curvature $H$ satisfies $H(p)=\alpha |p|^{-2} \langle\nu,p\rangle$, $p\in\Sigma$. These surfaces generalize in dimension two a classical…

In [15] the authors proved the Pugh-Shub conjecture for partially hyperbolic diffeomorphisms with 1-dimensional center, i.e. stable ergodic diffeomorphism are dense among the partially hyperbolic ones. In this work we address the issue of…

The special isothermic surfaces, discovered by Darboux in connection with deformations of quadrics, admit a simple explanation via the gauge-theoretic approach to isothermic surfaces. We find that they fit into a heirarchy of special…

The present paper deals with some characterizations of rectifying and osculating curves on a smooth surface with respect to the reference frame $\{\vec{T},\ \vec{N},\ \vec{T}\times\vec{N}\}$. We have computed the components of position…