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In 3-dimensional Euclidean space, the geometric figures of a regular curve are completely determined by the curvature function and the torsion function of the curve, and surfaces are the fundamental curved spaces for pioneering study in modern geometry as well as in classical differential geometry. In this paper, we define parametrizations for surface by using parametric functions whose images are in the normal plane of each point on a given curve, and then obtain some results relating the Gaussian curvature of the surface with curvature and torsion of the given curve. In particular, we find some conditions for the surface to have either nonpositive Gaussian curvature or nonnegative Gaussian curvature.
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참고문헌 (7)
참고문헌 신청
채영도 / 2006 / Tubes in singular spaces of nonpositive curvature / 대한수학회지 43(5):1129~1142
채영도 / 2007 / A lower bound for area of compact singular surfaces of nonpositive curvature / 대한수학회보 44(1):103~108
B. Y. Chen / 2003 / When does the position vector of a space curve always lie in its rectifying plane / Am. Math. Mon 110:147~152
H. Liu / 2004 / Curves in the lightlike cone / Contrib. Algebr. Geom 45:291~303
H. Liu / 2011 / Representation formulas of curves in a 2 and 3 dimensional lightlike cone / Results Math 59:437~451
채영도 / 2007 / A lower bound for area of compact singular surfaces of nonpositive curvature / 대한수학회보 44(1):103~108
B. Y. Chen / 2003 / When does the position vector of a space curve always lie in its rectifying plane / Am. Math. Mon 110:147~152
H. Liu / 2004 / Curves in the lightlike cone / Contrib. Algebr. Geom 45:291~303
H. Liu / 2011 / Representation formulas of curves in a 2 and 3 dimensional lightlike cone / Results Math 59:437~451
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