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.
Keywords:
manifold, affine connection, torsion, quasiplanar map, deformation tensorHow to Cite
Verhóczki, L. “QUASIPLANAR MAPS BETWEEN THREE-DIMENSIONAL MANIFOLDS ”, Periodica Polytechnica Mechanical Engineering, 36(3-4), pp. 279–290, 1992.
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