I will begin with recalling former results on Green-Griffiths-Lang (GGL) Conjecture and its strong form, which was proposed in 1980s. In the surface case, i.e., $dim = 2$ , there are results due to Lu-Yau (1990) and McQuillan (1998) in terms of $C_{1}$ and $C_{2}$ . Still, the general case is open now.

In terms of irregularity compared with the dimension we recall the log-Bloch-Ochiai (1981), N.- Winkelmann-Yamanoi and Lu-Winkelmann. It is noted that the recent preprint due to Cadorel-Den-Yamanoi establishes the strong GGL Conjecture in the case of the maximal Albanese dimension.

Without irregularity in general dimension, we discuss to introduce Wronskian and Wronskian curvature associated to a $C^{\infty }$ -connection in the holomorphic tangent bundle. Even if it is not holomorphic, Lemma on logarithmic derivative type remains hold. Then defining its curvature, we discuss the Wronskian degeneration of entire curves. If the idea is applied to $\mathbb{P}^{n}$ , Cartan’s SMT is recovered (N. 2011). Some open problems will be discussed.