Lines of principal curvature on canal surfaces in R3.
نویسندگان
چکیده
In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R3. By means of a connection of the differential equations for these curvature lines and real Riccati equations, it is established that canal surfaces have at most two isolated periodic principal lines. Examples of canal surfaces with two simple and one double periodic principal lines are given.
منابع مشابه
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In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R. By means of a connection of the differential equations for these curvature lines and real Riccati equations, it is established that canal surfaces have at most two isolated ...
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ورودعنوان ژورنال:
- Anais da Academia Brasileira de Ciencias
دوره 78 3 شماره
صفحات -
تاریخ انتشار 2006