Conformal and rank-one deformations of Riemannian metrics with tangent two-planes of zero curvature on a compact manifold (Q1876456)

The authors study Riemannian metrics on a compact manifold which have tangent two-planes of zero sectional curvature at each point of this manifold. They prove that the tangent two-planes of zero sectional curvature cannot disappear completely under sufficiently large classes of deformations. This is an English translation of the author's article published in the book [\textit{Yu. G. Reshetnyak} (ed.) et al., Proceedings of the conference `Geometry and applications' dedicated to the 70th anniversary of Prof. Victor Toponogov. Novosibirsk: Izdatel'stvo Instituta Matematiki (2001; Zbl 0990.53031)].