On the global real analyticity of solutions to on compact manifolds

Real analyticity of the canonical versal deformations of CR-structures

“…(see Proposition 1 in [Tar1]). So, using this T , we newly introduce a C ∞ vector bundle decompostion…”

“…From now on, we adopt this supplement vector field T and use the Levi-form according to (1.2). And following [Tar1], we use the notaion W = 0 T + 0 T .…”

“…Therefore by Lemma 1 in [Tar1], we have that φ(t) is real analytic for any t in (0, ). And by the following lemma, it is shown that φ(t) is real analytic.…”

“…This nonlinear equations' principal part is subelliptic, and we note that in the nonlinear term, only Xφ(t), XY φ(t), where X, Y in 0 T + 0 T , terms appear. Of course if there is no nonlinear term in this equation, the solution must be real analytic (M being real analytic, so real analytic hypo-ellipticity holds) (see [Tar1], [Ko]). In our case, as the non linear term is quite suitable (it doesn't include XT φ(t) term and T T φ(t) term, where X in 0 T + 0 T and T is the missing direction), it is natural to expect the same result as in the elliptic case.…”

“…We show that this φ(t) is real analytic. We follow the Tartakoff's line in [Tar1] and we adopt his notations. Let p o be the reference point of M .…”