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We describe some properties of noncompact Euclidean cone manifolds with coneangles less than c less than 2pi and singular locus a submanifold. Moreprecisely, we describe its structure outside a compact set. As a corollary weclassify those with cone angles less than 3pi/2 and those with all cone anglesequal to 3pi/2.

Non compact Euclidean cone 3-manifolds with cone angles less than 2pi