Brauer-Manin obstruction for Wehler K3 surfaces of Markoff type

Following a recent work of Fuchs, Litman, Silverman, and Tran, we study the Brauer-Manin obstruction for integral points on Wehler K3 surfaces of Markoff type. In particular, we construct some families which fail the integral Hasse principle via the Brauer-Manin obstruction with some counting results of similar nature to those in recent works of Ghosh and Sarnak; Loughran and Mitankin; and Colliot-Th & eacute;l & egrave;ne, Wei, and Xu. We also give some counterexamples to strong approximation which can be explained by the Brauer-Manin obstruction, and study a few aspects of rational points on affine surfaces.