Copositivity for 3rd-Order Symmetric Tensors and Applications

The strict opositivity of 4th order symmetric tensor may apply to detect vacuum stability general scalar potential. For finding analytical expressions (strict) tensor, we reduce its 3rd better deal with it. So, it is provided that several analytically sufficient conditions for the copositivity 3th 2 dimensional (3 dimensional) tensors. Subsequently, applying these conclusions tensors, are proved and 3 Finally, results present $\mathbb{Z}_3$ dark matter.