Global sections of twisted normal bundles of K3 surfaces and their hyperplane sections

Let $S\subset {\mathbb{P}}^g$ be a smooth $K3$ surface of degree $2g-2$, $g \geq 3$\mathrm{.}Weclassifyallthecasesforwhich$h^0($\mathcal{N}${S/$\mathbb{P}$^g}(-2)) \neq 0$andthecasesforwhich$h^0($\mathcal{N}${S/$\mathbb{P}$^g}(-2)) < h^0($\mathcal{N}$_{C/$\mathbb{P}$^{g-1}}(-2))$for$C \subset $\mathbb{P}$^{g-1}$ a general canonical curve section of $S$.