Godbillon-Vey type functional for 3-dimensional almost contact manifolds (Q6617358)

In this very interesting paper, the author introduces a Godbillon-Vey type functional for three-dimensional almost contact manifolds, presents it in Reinhart-Wood form, and derives its Euler-Lagrange equations for all variations that preserve the structure vector field. Moreover, the author constructs some critical three-dimensional almost contact manifolds (with respect to the new functional) that exhibit a double-twisted product structure. These solutions belong to the class \(C_5\oplus C_{12}\) in the Chinea-Gonzalez classification.