Holomorphic maps from Sasakian manifolds into Kähler manifolds

Abstract

The authors consider ±(Φ, J)-holomorphic maps from Sasakian manifolds into Kähler manifolds, which can be seen as counterparts of holomorphic maps in Kähler 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.

Keywords

Sasakian manifold / Harmonic / Schwarz lemma / Homotopic invariant

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