arXiv subjects

Henri Anciaux

Publications and source records attributed to Henri Anciaux.

21 records · Page 2Linked to original sources

arXiv2008

Cyclic and ruled Lagrangian surfaces in complex Euclidean space

We study those Lagrangian surfaces in complex Euclidean space which are foliated by circles or by straight lines. The former, which we call cyclic, come in three types, each one being described by means of, respectively, a planar curve, a Legendrian curve of the 3-sphere or a Legendrian curve of the anti de Sitter 3-space. We also describe ruled Lagrangian surfaces. Finally we characterize those cyclic and ruled Lagrangian surfaces which are solutions to the self-similar equation of the Mean Curvature Flow. Finally, we give a partial result in the case of Hamiltonian stationary cyclic surfaces.

math.DG↗

arXiv2004

Lagrangian submanifolds foliated by (n-1)-spheres in R^2n

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 is special Lagrangian, self-similar or Hamiltonian stationary. In all these cases, the submanifold is centered, i.e. invariant under the action of SO(n). It suffices then to solve a simple ODE in two variables to describe the geometry of the solutions.

math.DG↗

arXiv2003

Special Lagrangian submanifolds in the complex sphere

We construct a family of Lagrangian submanifolds in the complex sphere with a SO(n)-invariance property. Among them we find those which are special Lagrangian with respect with the Calabi-Yau structure defined by the Stenzel metric.

math.DG↗