  9We consider complex structures with totally real zero section of the tangent
bundle. We assume that the complex structure tensor is real-analytic along the
fibers of the tangent bundle. This assumption is quite natural in view of a
well known existence result by Bruhat and Whitney. We provide explicit
integrability equations for such complex structures in terms of the fiberwise
Taylor expansion. In a particular geometric case considered in the literature,
we explicit much further the fiberwise Taylor expansion of the complex
structure as well as the integrability equations.
