Holomorphic Maps from Sasakian Manifolds into Khler Manifolds

The authors consider ±(Φ, J)-holomorphic maps from Sasakian manifolds into Ka¨hler manifolds, which can be seen as counterparts of holomorphic maps in Ka¨hler geometry. It is proved that those maps must be harmonic and basic. Then a Schwarz lemma for those maps is obtained. On the other hand, an invariant in its basic homotopic class is obtained. Moreover, the invariant is just held in the class of basic maps.