Abstract
In this paper, we study Riemannian, anti-invariant and Lagrangian submersions from locally product Riemannian manifolds onto Riemannian manifolds. We first give a characterization theorem for Riemannian submersions. It is proved that the fibers of a Lagrangian submersion are always totally geodesic. We also consider the first variational formula of anti-invariant Riemannian submersions and give a new condition for the harmonicity of such submersions.
Original language | English |
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Pages (from-to) | 411-422 |
Number of pages | 12 |
Journal | Journal of Geometry |
Volume | 108 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jul 2017 |
Bibliographical note
Publisher Copyright:© 2016, Springer International Publishing.
Keywords
- anti-invariant submersions
- first variational formula
- horizontal distribution
- Lagrangian submersion
- locally product Riemannian manifold
- Riemannian submersion