On new examples of Hamiltonian-minimal and minimal Lagrangian submanifolds in $C^n$ and $CP^n$

Details On new examples of Hamiltonian-minimal and minimal Lagrangian submanifolds in $C^n$ and $CP^n$ On new examples of Hamiltonian-minimal and minimal Lagrangian submanifolds in $C^n$ and $CP^n$

2003-09-07

arxiv.org/abs/math/0309128v1

Mathematics

Differential Geometry

16 pages

Scientific paper

We propose a new method for the construction of Hamiltonian-minimal and minimal Lagrangian immersions of some manifolds in $C^n$ and in $CP^n$. By this method one can construct, in particular, immersions of such manifolds as the generalized Klein's bottle $K^n$, the multidimensional torus, $K^{n-1}\times S^1$, $S^{n-1}\times S^1$, and others. In some cases these immersions are embeddings. For example, it is possible to embed the following manifolds: $K^{2n+1},$ $S^{2n+1}\times S^1$, $K^{2n+1}\times S^1$, $S^{2n+1}\times S^1\times S^1$.

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