In the 3-dimensional Euclidean space E3, a quadric surface is either ruled or of one following two kinds z2=as2+bt2+c,abc≠0 z=a2s2+b2t2,a>0,b>0. present paper, we investigate these three surfaces whose Gauss map N satisfies property ΔIIN=ΛN, where Λ square symmetric matrix order 3, and ΔII denotes Laplace operator second fundamental form II surface. We prove that spheres with nonzero Λ, h...

In this paper, firstly the ruled surface drawn by Darboux vector is expressed as a quaternion. Then, spatial quaternionic definition of striction curve given and integral invariants are calculated. Finally, which corresponds to dual derived with help quaternions obtained.

The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...