QUASIPLANAR MAPS BETWEEN THREE-DIMENSIONAL MANIFOLDS

Abstract

The problem of quasiplanar maps between spaces with affine connection was set by N. S. SZINYUKOV in [4]. Quasiplanar maps can be regarded as generalizations of maps of affine spaces which preserve plane curves. In this paper we study a special class of quasiplanar maps between three-dimensional manifolds. Among others we give a sufficient and necessary condition for a map to be quasiplanar. Our main results are analogous to the results of SZINYUKOV and J. MIKES who studied in [2] quasiplanar maps in spaces with more than three dimensions.