Certain classifications on quadrics in simply isotropic space ${\mathbb{I}}^3$

In this paper, we deal with the natural geometry of quadric surfaces in the isotropic space ${\mathbb{I}}^3$. We provided defining equations for the $3^{rd},4^{th}$ type ruled surfaces and $1^{st},2^{nd}$ type of quadric surfaces. In this paper, we investigated the finite Chen-type of ruled and quadric surfaces in the 3-dimensional simply isotropic space ${\mathbb{I}}^3$, corresponding to the third fundamental form of the surface.