R n on n -manifolds]]>

摘要

AbstractThis paper contains some results on the topology of a nondegenerate action ofRnon a compact connectedn-manifoldMwhen the action is totally hyperbolic (i.e. its toric degree is zero). We study theR-action generated by a fixed vector ofRn, that provides some results on the number of hyperbolic domains and the number of fixed points of the action. We study with more details the case of the 2-sphere, in particular we investigate some combinatorial properties of the associated 4-valent graph embedded inS2. We also construct hyperbolic actions in dimension 3, on the sphereS3and on the projective spaceRP3.]]>