Non-existence of harmonic maps on trans-Sasakian manifolds

Abstract

In this paper, we have studied harmonic maps on trans-Sasakian manifolds. First it is proved that if F: M₁ → M₂ is a Riemannian ϕ-holomorphic map between two trans-Sasakian manifolds such that ξ₂ ∈ (Im dF)^⊥, then F can not be harmonic provided that β₂ ≠ 0. We have also found the necessary and sufficient condition for the harmonic map to be constant map from Kaehler to trans-Sasakian manifold. Finally, we prove the non-existence of harmonic map from locally conformal Kaehler manifold to trans-Sasakian manifold.