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All non-twisting Petrov-type N solutions of vacuum Einstein field equationswith cosmological constant Lambda are summarized. They are shown to belongeither to the non-expanding Kundt class or to the expanding Robinson-Trautmanclass. Invariant subclasses of each class are defined and the correspondingmetrics are given explicitly in suitable canonical coordinates. Relationsbetween the subclasses and their geometrical properties are analyzed. In thesubsequent paper these solutions are interpreted as exact gravitational wavespropagating in de Sitter or anti-de Sitter spacetimes.Comment: 16 pages, no figures, LaTeX, To appear in J. Math. Phy

Gravitational waves in vacuum spacetimes with cosmological constant. I. Classification and geometrical properties of nontwisting type N solutions