In this note we suggest a construction of the Morse-Novikov theory for a class of non-transversal gradients and generalize to this class the basic results of the classical Morse-Novikov theory including its non-abelian version.
"Dynamics of gradient flows in the half-transversal Morse theory." Proc. Japan Acad. Ser. A Math. Sci. 85 (1) 6 - 10, January 2009. https://doi.org/10.3792/pjaa.85.6