Let $(M,J,g,\omega)$ be a $2n$-dimensional almost Hermitian manifold. We extend the definition of Bott-Chern Laplacian on $(M,J,g,\omega)$, proving that it is still elliptic. On compact K\"ahler manifold, kernels Dolbeault and coincide. show such property does not hold when providing an explicit structure Kodaira-Thurston Furthermore, if connected $4$-manifold, denoting by $h^{1,1}_{BC}$ dimens...

In this paper, we give a necessary and sufficient condition for generalized real Bott manifold to have spin structure in terms of column vectors the associated matrix. We also an interpretation result acyclic $\omega$-weighted digraphs. Using this, obtain family manifolds that does not admit structure.