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This paper is concerned with the classifications of quadric surfaces of first and second kinds in Euclidean 3-space satisfying the Jacobi condition with respect to their curvatures, the Gaussian curvature K, the mean curvature H, second mean curvature $H_{II}$ and second Gaussian curvature $K_{II}$. Also, we study the zero and non-zero constant curvatures of these surfaces. Furthermore, we investigated the (A, B)-Weingarten, (A, B)-linear Weingarten as well as some special ($C^2$, K) and $(C^2,\;K{\sqrt{K}})$-nonlinear Weingarten quadric surfaces in $E^3$, where $A{\neq}B$, A, $B{\in}{K,H,H_{II},K_{II}}$ and $C{\in}{H,H_{II},K_{II}}$. Finally, some important new lemmas are presented.
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참고문헌 (23)
참고문헌 신청
J. Weingarten / 1861 / Ueber eine Klasse auf einander abwickelbarer Flaachen / J. Reine Angew. Math 59:382~393
J.Weingarten / 1863 / Ueber die Flachen derer Normalen eine gegebene Flache beruhren / J. Reine Angew. Math 62:61~63
Van-Brunt / 1996 / Potential applications of Weingarten surfaces in CAGD, Part I: Weingarten surfaces and surface shape investigation / Comput. Aided Geom. Des 13:569~582
W. Kuhnel / 1994 / Ruled W-surfaces / Arch. Math 62:475~480
D. W. Yoon / 2002 / Some properties of the helicoid as ruled surfaces / JP J. Geom. Topology 2(2):141~147
J.Weingarten / 1863 / Ueber die Flachen derer Normalen eine gegebene Flache beruhren / J. Reine Angew. Math 62:61~63
Van-Brunt / 1996 / Potential applications of Weingarten surfaces in CAGD, Part I: Weingarten surfaces and surface shape investigation / Comput. Aided Geom. Des 13:569~582
W. Kuhnel / 1994 / Ruled W-surfaces / Arch. Math 62:475~480
D. W. Yoon / 2002 / Some properties of the helicoid as ruled surfaces / JP J. Geom. Topology 2(2):141~147
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