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    Scalar curvature of Lagrangian Riemannian submersions and their harmonicity
    (World Scientific Publ Co Pte Ltd, 2017) Meric, Semsi Eken; Kilic, Erol; Sagiroglu, Yasemin
    In this paper, we consider a Lagrangian Riemannian submersion from a Hermitian manifold to a Riemannian manifold and establish some basic inequalities to obtain relationships between the intrinsic and extrinsic invariants for such a submersion. Indeed, using these inequalities, we provide necessary and sufficient conditions for which a Lagrangian Riemannian submersion pi has totally geodesic or totally umbilical fibers. Moreover, we study the harmonicity of Lagrangian Riemannian submersions and obtain a characterization for such submersions to be harmonic.