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We propose a new method for the construction of Hamiltonian-minimal andminimal Lagrangian immersions of some manifolds in $C^n$ and in $CP^n$. By thismethod one can construct, in particular, immersions of such manifolds as thegeneralized Klein's bottle $K^n$, the multidimensional torus, $K^{n-1}\timesS^1$, $S^{n-1}\times S^1$, and others. In some cases these immersions areembeddings. For example, it is possible to embed the following manifolds:$K^{2n+1},$ $S^{2n+1}\times S^1$, $K^{2n+1}\times S^1$, $S^{2n+1}\timesS^1\times S^1$.Comment: 16 page

New examples of Hamilton-minimal and minimal Lagrangian manifolds in $ \mathbb C^n$ and $ \mathbb C\mathrm P^n$