Ruled Special Lagrangian 3‐Folds In C 3

Ruled Minimal Lagrangian Submanifolds of Complex Projective 3-space

We show how a ruled minimal Lagrangian submanifold of complex projective 3-space may be used to construct two related minimal surfaces in the 5-sphere.

2 00 3 Second Order Families of Special Lagrangian Submanifolds in C

This paper extends to dimension 4 the results in the article " Second Order Families of Special Lagrangian 3-folds " by Robert Bryant. We consider the problem of classifying the special Lagrangian 4-folds in C 4 whose fundamental cubic at each point has a nontrivial stabilizer in SO(4). Points on special Lagrangian 4-folds where the SO(4)-stabilizer is nontrivial are the analogs of the umbilica...

Special Lagrangian m-folds in C^m with symmetries

Special Lagrangian cones in C³ and primitive harmonic maps

In this article I show that every special Lagrangian cone in C determines, and is determined by, a primitive harmonic surface in the 6symmetric space SU3/SO2. For cones over tori, this allows us to use the classification theory of harmonic tori to describe the construction of all the corresponding special Lagrangian cones. A parameter count is given for the space of these, and some of the examp...

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 in the 3-sphere or a Legendrian curve in the anti-de Sitter 3-space. We describe ruled Lagrangian surfaces and characterize the cyclic and ru...