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Some characterizations of canal surfaces

Huili Liu|Jinhua Qian|YOUNG HO KIM
대한수학회 (The Korean Mathematical Society)|2016.03|대한수학회보 (Bulletin of the KMS)|제53권 제2호|pp. 461-477

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참고문헌

키워드

mean curvatureGaussian curvatureWeingarten surfacecanal surfacelinear Weingarten surfacesecond Gaussian curvature
주제분류수학

초록

This work considers a particular type of swept surface named canal surfaces in Euclidean 3-space. For such a kind of surfaces, some interesting and important relations about the Gaussian curvature, the mean curvature and the second Gaussian curvature are found. Based on these relations, some canal surfaces are characterized.

Abstract

This work considers a particular type of swept surface named canal surfaces in Euclidean 3-space. For such a kind of surfaces, some interesting and important relations about the Gaussian curvature, the mean curvature and the second Gaussian curvature are found. Based on these relations, some canal surfaces are characterized.

참고문헌 (11)

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  2. S. Haesen, "The mean curvature of the second funda-mental form", Houston J. Math, 34(3), pp.703~719 (2008)
  3. Y. H. Kim, "On non-developable ruled surface in Lorentz-Minkowski 3-spaces", Taiwanese J. Math, 11(1), pp.197~214 (2007)
  4. S. N. Krivoshapko, "Classification of cyclic surfaces and geomet-rical research of canal surfaces", Int. J. Res. Rev. Appl. Sci, 12(3), pp.360~374 (2012)
  5. R. Lopez, "Linear Weingarten surfaces in Euclidean and hyperbolic space", Mat. Contemp, 35, pp.95~113 (2008)
  6. R. Lopez, "Rotational linear Weingarten surfaces of hyperbolic type", Israel J. Math, 167, pp.283~302 (2008)
  7. T. Maekawa, "Analysis and applications of pipe surfaces", Comput. Aided Geom. Design, 15(5), pp.437~458 (1998)
  8. A. D. Polyanin, "Handbook of Exact Solutions for Ordinary Differential Equations", pp.2003, Chapman and Hall
  9. Jin Suk Ro, "TUBES OF WEINGARTEN TYPES IN A EUCLIDEAN 3-SPACE", 충청수학회지, 22(3), pp.359~366 (2009), 충청수학회
  10. S. Verpoort, "The Geometry of the Second Fundamental Form: Curvature Properties and Variational Aspects", PhD, pp.2008
  11. Z. Q. Xu, "Analytic and algebraic properties of canal surfaces", J. Comput. Appl. Math, 195(1-2), pp.220~228 (2006)

관련 논문AI추천

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