Right Conoid in Euclidean 3-Space


KARACAN M. K., YÜKSEL N., TUNCER Y., SALTIK B.

XVI. Uluslararası Geometri Sempozyum, Manisa, Turkey, 4 - 07 July 2018, pp.250

  • Publication Type: Conference Paper / Summary Text
  • City: Manisa
  • Country: Turkey
  • Page Numbers: pp.250
  • Erciyes University Affiliated: Yes

Abstract

In this study, the conditions for the Right Conoid Surface to be flat and minimal are determined. Then, by using Gauss and mean curvature with second Gauss and mean curvature of surface, the conditions for Right Conoid Surface being Weingarten, linear Weingarten and quadratic are researched. Furthermore, we classify Right Conoid in the three-dimensional Euclidean space 3 E satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the first, the second and the third fundamental forms of the Right Conoid. We also give explicit forms of this surfaces. Keywords: Right Conoid; Second Gaussian curvature; Second mean curvature; Weingarten equation; Linear Weingarten equation; Laplacian operators; Quadric surface.