Scalar curvature of Lagrangian Riemannian submersions and their harmonicity
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, vol.14, no.12, 2017 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 14 Issue: 12
- Publication Date: 2017
- Doi Number: 10.1142/s0219887817501717
- Journal Name: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Karadeniz Technical University Affiliated: Yes
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 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.