کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4606528 1337710 2009 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Rotational hypersurfaces of periodic mean curvature
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Rotational hypersurfaces of periodic mean curvature
چکیده انگلیسی

In this paper we discuss rotational hypersurfaces in RnRn and more specifically rotational hypersurfaces with periodic mean curvature function. We show that, for a given real analytic function H(s)H(s) on RR, every rotational hypersurface M   in RnRn with mean curvature H(s)H(s) can be extended infinitely in the sense that all coordinate functions of the generating curve of M   are defined on all of RR as well. For rotational hypersurfaces with periodic mean curvature we present a criterion characterizing the periodicity of such hypersurfaces in terms of their mean curvature function. We also discuss a method to produce families of periodic rotational hypersurfaces where each member of the family has the same mean curvature function. In fact, given any closed planar curve with curvature κ, we prove that there is a family of periodic rotational hypersurfaces such that the mean curvature of each element of the family is explicitly determined by κ  . Delaunay's famous result for surfaces of revolution with constant mean curvature is included here as the case where n=3n=3 and κ is constant.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Differential Geometry and its Applications - Volume 27, Issue 6, December 2009, Pages 702–712
نویسندگان
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