Note About Hamiltonian Formalism of Modified $F(R)$ Ho\v{r}ava-Lifshitz Gravities and Their Healthy Extension

This note is devoted to the study of Hamiltonian formalism of modified F® Horava-Lifshitz theories of gravity that were proposed recently in arXiv:1001.4102[hep-th]. We also study Hamiltonian formulation of the healthy extended Horava-Lifshitz gravities and show that these theories have many unusual and interesting properties.