25 citations · 58 across the 19 of their papers we have counts for
21 papers
Quadric surfaces of revolution in the 3-sphere as cubic Weingarten surfaces
Ildefonso Castro, Daniel López-López
The study of quadric surfaces of revolution is a cornerstone of classical Euclidean geometry, but its extension to the three-dimensional sphere has not been sufficie…
Isometric immersions into three-dimensional unimodular metric Lie groups
Ildefonso Castro, José M. Manzano, José S. Santiago
We study isometric immersions of surfaces into simply connected 3-dimensional unimodular Lie groups endowed with either Riemannian or Lorentzian left-invariant metrics, assuming th…
Helicoidal minimal surfaces in the 3-sphere: An approach via spherical curves
Ildefonso Castro, Ildefonso Castro-Infantes, Jesús Castro-Infantes
We prove an existence and uniqueness theorem about spherical helicoidal (in particular, rotational) surfaces with prescribed mean or Gaussian curvature in terms of a continuous fun…
A new approach to rotational Weingarten surfaces
Paula Carretero, Ildefonso Castro
Weingarten surfaces are those whose principal curvatures satisfy a functional relation, whose set of solutions is called the curvature diagram or the W-diagram of the surface. Maki…
Spherical curves whose curvature depends on distance to a great circle
Ildefonso Castro, Ildefonso Castro-Infantes, Jesús Castro-Infantes
Motivated by a problem posed by David A. Singer in 1999 and by the elastic spherical curves, we study the spherical curves whose curvature is expressed in terms of the distance to…
Curves in Lorentz-Minkowski plane with curvature depending on their position
Ildefonso Castro, Ildefonso Castro-Infantes, Jesús Castro-Infantes
Motivated by the classical Euler elastic curves, David A. Singer posed in 1999 the problem of determining a plane curve whose curvature is given in terms of its position. We propou…
Evolution by mean curvature flow of Lagrangian spherical surfaces in complex Euclidean plane
Ildefonso Castro, Ana M. Lerma, Vicente Miquel
We describe the evolution under the mean curvature flow of embedded Lagrangian spherical surfaces in the complex Euclidean plane . In particular, we answer the Questi…
Homothetic solitons for the inverse mean curvature flow
Ildefonso Castro, Ana M. Lerma
We study solutions to the inverse mean curvature flow which evolve by homotheties of a given submanifold with arbitrary dimension and codimension. We first show that the closed one…
A new construction of Lagrangians in the complex Euclidean plane in terms of planar curves
Ildefonso Castro, Ana M. Lerma
We introduce a new method to construct a large family of Lagrangian surfaces in complex Euclidean plane by means of two planar curves making use of their usual product as complex f…
The Clifford torus as a self-shrinker for the Lagrangian mean curvature flow
Ildefonso Castro, Ana M. Lerma
We provide several rigidity results for the Clifford torus in the class of compact self-shrinkers for Lagrangian mean curvature flow.
Translating solitons for Lagrangian mean curvature flow in complex Euclidean plane
Ildefonso Castro, Ana M. Lerma
Using certain solutions of the curve shortening flow, including self-shrinking and self-expanding curves or spirals, we construct and characterize many new examples of translating…
Hamiltonian stationary self-similar solutions for Lagrangian mean curvature flow in complex Euclidean plane
Ildefonso Castro, Ana M. Lerma
We classify all Hamiltonian stationary Lagrangian surfaces in complex Euclidean plane which are self-similar solutions of the mean curvature flow.
Construction of Hamiltonian-minimal Lagrangian submanifolds in complex Euclidean space
Henri Anciaux, Ildefonso Castro
We describe several families of Lagrangian submanifolds in the complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian…
On Hamiltonian stationary Lagrangian spheres in non-Einstein Kaehler surfaces
Ildefonso Castro, Francisco Torralbo, Francisco Urbano
Hamiltonian stationary Lagrangian spheres in Kaehler-Einstein surfaces are minimal. We prove that in the family of non-Einstein Kaehler surfaces given by the product …
Lagrangian surfaces in complex Euclidean plane via spherical and hyperbolic curves
Ildefonso Castro, Bang-yen Chen
We present a method to construct a large family of Lagrangian surfaces in complex Euclidean plane by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equ…
Minimal Lagrangian surfaces in
Ildefonso Castro, Francisco Urbano
We deal with the minimal Lagrangian surfaces of the Einstein-Kähler surface , studying local geometric properties and showing that they can be locally described as…
Hamiltonian-minimal Lagrangian submanifolds in complex space forms
Ildefonso Castro, Haizhong Li, Francisco Urbano
Using Legendrian immersions and, in particular, Legendre curves in odd dimensional spheres and anti De Sitter spaces, we provide a method of construction of new examples of Hamilto…
On a new construction of special Lagrangian immersions in complex Euclidean space
Ildefonso Castro, Francisco Urbano
We construct new special Lagrangian submanifolds in complex Euclidean space using a pair of minimal Legendrian submanifolds in odd-dimensional spheres and certain Lagrangian surfac…
Lagrangian submanifolds foliated by (n-1)-spheres in R^2n
Henri Anciaux, Ildefonso Castro, Pascal Romon
We study Lagrangian submanifolds foliated by (n-1)-spheres in R^2n for n>2. We give a parametrization valid for such submanifolds, and refine that description when the submanifold…
Lagrangian surfaces with circullar ellipse of curvature in complex space forms
Ildefonso Castro
We classify the Lagrangian orientable surfaces in complex space forms with the property that the ellipse of curvature is always a circle. As a consequence, we obtain new characteri…
Minimal Lagrangian submanifolds in the complex hyperbolic space
I. Castro, C. R. Montealegre, F. Urbano
In this paper we construct new examples of minimal Lagrangian submanifolds in the complex hyperbolic space with large symmetry groups, obtaining three 1-parameter families with coh…