Tubes in Singular Spaces of Nonpositive Curvature

Chai, Y. D.; Lee, Doohann

doi:10.4134/jkms.2006.43.5.1129

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2014

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“…Also, intrinsic surfaces are the fundamental curved spaces for pioneering study in modern geometry as well as in classical differential geometry [1], [2].…”

Section: Introductionmentioning

confidence: 99%

A Note on Surfaces in the Normal Bundle of a Curve

Lee¹,

Huang²

2014

Journal of the Chungcheong Mathematical Society

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Abstract. 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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“…Also, intrinsic surfaces are the fundamental curved spaces for pioneering study in modern geometry as well as in classical differential geometry [1], [2].…”

Section: Introductionmentioning

confidence: 99%

A Note on Surfaces in the Normal Bundle of a Curve

Lee¹,

Huang²

2014

Journal of the Chungcheong Mathematical Society

View full text Add to dashboard Cite

show abstract

Tubes in Singular Spaces of Nonpositive Curvature

Cited by 1 publication

References 7 publications

A Note on Surfaces in the Normal Bundle of a Curve

A Note on Surfaces in the Normal Bundle of a Curve

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