Geometry and singularities of spatial and spherical curves

Date
2004
Authors
Xiong, Jianfei
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Abstract
In the first part of this dissertation the spherical evolute, the spherical involute, the spherical orthotomic and the spherical antiorthotomic are investigated and their local diffeomorphic types are determined. The concept of the spherical conic is introduced. It is proven that the incident angle and reflection angle are equal for the spherical conic. The necessary and sufficient conditions for the spherical conic to be a circle are given. In the second part of this dissertation the ruled surfaces of normals and binormals of a regular space curve are locally classified under the left-right action according to the types of the curve. For this purpose some results are obtained on the relationship of the powers of terms in the Taylor series of an invertible function and its inverse.
Description
Mode of access: World Wide Web.
Thesis (Ph. D.)--University of Hawaii at Manoa, 2004.
Includes bibliographical references (leaves 113-114).
Electronic reproduction.
Also available by subscription via World Wide Web
vii, 114 leaves, bound ill. 29 cm
Keywords
Sphere, Conics, Spherical
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