ON SOME GEOMETRIC PROPERTIES OF QUADRIC SURFACES IN EUCLIDEAN SPACE

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.