Title: On Rigidity and the Albanese Variety for Parallelizable Manifolds
Abstract: We study the rigidity questions and the Albanese Variety for Complex Parallelizable Manifolds. Both are related to the study of the cohomology group $H^1(X,\mathcal O)$. In particular we show that a compact complex parallelizable manifold is rigid iff $b_1(X)=0$ iff Alb$(X)=\{e\}$ iff $H^1(X,\mathcal O)=0$.