Delaunay Type Surfaces In A Randers Space

The surfaces with constant mean curvature in Euclidean space,especially the surfaces with constant mean curvature in three-dimensional space,have been studied extensively.In 1841,C.Delaunay classified the rotation surfaces with constant mean curvature inR~3.Apart form planes,spheres,cylinders,and the minimal cateoids,he gave unduloid surfaces and nodoid surfaces.This parper considers a class of Minkowski-Randers space(R~3,(?)_b).R~3 is Euclidean space with a Randers metric _bF=a+b,in whichais the Euclidean metric,andbis a constant one form.This parper studies the shape of a non-zero constant mean curvature rotation surfaces(i.e.Delaunay type surface)in the Randers space(R~3,(?)_b)generated by plane curves rotating around the?~# direction under the Busemann-Hausdorff measure.Firstly,this parper gives the formula of mean curvature form of a Finsler submanifold,and calculates the mean curvature of the hypersurface formed rotating the plane curve around the?~# direction in(R~3,(?)_b),then derives the equation that characterizes the rotational cmc surface.Through analyzing the influence of different values of b on the surface in detail and classifying the Delaunay surfaces with the rotation axis of?~#,this paper obtains explicit expressions and draws the graphs.