Reductions of minimal Lagrangian submanifolds with symmetries

Deformations of Minimal Lagrangian Submanifolds with Boundary

Let L be a special Lagrangian submanifold of R with boundary lying on the symplectic, codimension 2 submanifold W . It is shown how deformations of L which keep the boundary of L confined to W can be described by an elliptic boundary value problem, and two results about minimal Lagrangian submanifolds with boundary are derived using this fact. The first is that the space of minimal Lagrangian s...

On the Lifts of Minimal Lagrangian Submanifolds

Bryant and Salamon constructed metrics with holonomy G2 and Spin(7) on spin bundles of 3-dimensional space forms, and spin bundles and bundles of anti-self-dual 2-forms on self-dual Einstein 4-manifolds [BrS]. Since, apart from holonomy, the construction of integrable G2(respectively Spin(7)) structures amounts to finding differential 3(4)forms of generic type on 7(8) manifolds satisfying appro...

Minimal Lagrangian Submanifolds in Complex Euclidean Space

Holomorphic vector fields and minimal Lagrangian submanifolds

The purpose of this note is to establish the following theorem: Let N be a Kahler manifold, L be an oriented immersed minimal Lagrangian submanifold of N without boundary and V be a holomorphic vector field in a neighbourhood of L in N . Let div(V ) be the (complex) divergence of V . Then the integral ∫ L div(V ) = 0. Vice versa suppose that N is Kahler-Einstein with non-zero scalar curvature a...

Hamiltonian-minimal Submanifolds in Kaehler Manifolds with Symmetries

By making use of the symplectic reduction and the cohomogeneity method, we give a general method for constructing Hamiltonian minimal submanifolds in Kaehler manifolds with symmetries. As applications, we construct infinitely many nontrivial complete Hamiltonian minimal submanifolds in CP n and Cn.