Abstract
AbstractIn this paper we prove the existence of complete minimal surfaces in some metric semidirect products. These surfaces are similar to the doubly and singly periodic Scherk minimal surfaces in ${ \mathbb{R} }^{3} $. In particular, we obtain these surfaces in the Heisenberg space with its canonical metric, and in ${\mathrm{Sol} }_{3} $ with a one-parameter family of nonisometric metrics.
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