X: J_t(x) \not= J_0(x) \} $ is contained in $U_1$;

c\) $M$ is $J_1$-holomorphic;

d\) all $\{J_t\}$ are tamed by the given form $\omega $, , $\omega(v,J_tv) > 0$ for every nonzero $v\in TX$.

Proof. Let $N$ be a normal bundle to $M$ in $X$ and $V_1$ a neighbourhood of the zero section in $N$. Shrinking $V_1$ and $U_1$ we can assume that $U_1$ is an image of $V_1$ under an $\exp$-map in $J$-Hermitian metric $h$ associated to $\omega $. More precisely, one should take the Riemannian metric associated to $h$, $g = \re h$. Shrinking $V_1$ and $U_1$ once more, if necessary, we can extend the distribution of tangent planes to $M =$ (zero section of $N$) to the distribution $\{ L_x\} _{x\in V_1}$ of $\omega $-positive planes on $V_1$. Here we do not distinguish between $\omega$ and its lift onto $V_1$ by $\exp$. Denote by $N_x$ the subspace in $T_xV_1$ which is $g$-orthogonal to $L_x$. Perturbing $g$ we can choose the distribution $\{ L_x\}$ in such a way that if $\exp(x)= \exp(y)$ for some $x\not= y$ from $V_1$ then $d\exp_x(L_x)=d\exp_y(N_y)$ and $d\exp_y(L_y)=d\exp_x(N_x)$. In particular, we suppose that $M$ intersects itself $g$-orthogonally. For every $x\in V_1$ choose an orthonormal 