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- Title
Scalar curvature of Lagrangian Riemannian submersions and their harmonicity.
- Authors
Eken Meri̇ç, Şemsi; Kiliç, Erol; Sağiroğlu, Yasemi̇n
- Abstract
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 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.
- Subjects
RIEMANNIAN submersions; RIEMANNIAN manifolds; RIEMANNIAN geometry; MANIFOLDS (Mathematics); SUBMERSIONS (Mathematics)
- Publication
International Journal of Geometric Methods in Modern Physics, 2017, Vol 14, Issue 12, p-1
- ISSN
0219-8878
- Publication type
Article
- DOI
10.1142/S0219887817501717