Anti-invariant Riemannian maps from almost Hermitian manifolds
Differential Geometry
2012-10-02 v1
Abstract
As a generalization of anti-invariant Riemannian submersions, we introduce anti-invariant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We give examples and investigate the geometry of foliations which are arisen from the definition of an anti-Riemannian map. Then we give a decomposition theorem for the source manifold of such maps. We also find necessary and sufficient conditions for anti-invariant Riemannian maps to be totally geodesic and show that every pluriharmonic Lagrangian Riemannian map, which is a special anti-invariant Riemannian map, from a K\"{a}hler manifold to a Riemannian manifold is totally geodesic.
Keywords
Cite
@article{arxiv.1210.0401,
title = {Anti-invariant Riemannian maps from almost Hermitian manifolds},
author = {Bayram Sahin},
journal= {arXiv preprint arXiv:1210.0401},
year = {2012}
}
Comments
12 pages. arXiv admin note: text overlap with arXiv:1012.2001, arXiv:1206.3563, arXiv:1206.3393