Spin-structures on real Bott manifolds with K\"ahler structures

Let M be a real Bott manifold with K"{a}hler structure. Using Ishida characterization we give necessary and sufficient condition for the existence of the Spin-structure on M. In proof we use the technic developed in Popko, Szczepa'{n}ski “Cohomological rigity of oriented Hantzsche-Wendt manifolds” (Adv. Math. 302 (2016), 1044 - 1068) and characteristic classes.