%0 Journal Article %T Rigidity and Vanishing Theorems in K-Theory I %A Kefeng Liu %A Xiaonan Ma %A Weiping Zhang %J Mathematics %D 1999 %I arXiv %R 10.1016/S0764-4442(00)00155-5 %X In this paper, we first establish a K-theory version of the equivariant family index theorem for a circle action, then use it to prove several rigidity and vanishing theorems on the equivariant K-theory level. %U http://arxiv.org/abs/math/9912108v1