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Conformal immersion of Riemannian products in low codimension

2018/11/13 by Guimarães, Felippe, Mendonça, Bruno
#53B25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.05570

Abstract

We proved that a conformal immersion of M0n0× M1n1 as an hipersurface in a Euclidean space must be an extrinsic product of immersions, under the assumption that n0, n1 ≥ 2 and that Mn00× Mn11 is not conformally flat. We also stated a similar theorem for an arbitrary number of factors, more precisely, a conformal immersion f\colon Mn00 × ⋯ × Mnkk → ℝn+k must be an extrinsic product of immersions if one of the factors admits a plane with vanishing curvature and the remaining factors are not flat.

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