ON RIGIDITY AND THE ALBANESE VARIETY FOR PARALLELIZABLE MANIFOLDS

JÖRG WINKELMANN

Abstract. We study the rigidity questions and the Albanese Variety for Complex Parallelizable Manifolds. Both are related to the study of the cohomology group H^{1}(X, O). In particular we show that a compact complex parallelizable manifold is rigid iff b_{1}(X) = 0 iff Alb(X) = {e} iff H^{1}(X, O) = 0.