The $CR$ analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with pseudo parallel pseudo mean curvature vector fields, will be characterized.
"$CR$ rigidity of pseudo harmonic maps and pseudo biharmonic maps." Hokkaido Math. J. 46 (2) 141 - 187, June 2017. https://doi.org/10.14492/hokmj/1498788016