On the Witten Rigidity Theorem for Stringc^c Manifolds

We establish the family rigidity and vanishing theorems on the equivariant $K$-theory level for the Witten type operators on String$^c$ manifolds introduced by Chen-Han-Zhang.Comment: arXiv admin note: substantial text overlap with arXiv:1104.3972, and with arXiv:math/0001014, arXiv:math/9912108 by other author