Abstract: In this thesis we consider the problem posed by Griffiths, which asks to determine which polynomials of Chern forms will be always positive for any Griffiths positive vector bundle $E$. Following an idea used in the work of Yau and Zheng, we explore the induced metric on the projectivized bundle, the Grothendieck equation and the push forward of forms and we are able to prove that the signed Segre forms are always positive.