1. Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures
- Creator:
- Ghosh, Amalendu
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Weyl manifold, Einstein-Weyl structure, and infinitesimal harmonic transformation
- Language:
- English
- Description:
- We prove that a connected Riemannian manifold admitting a pair of nontrivial Einstein-Weyl structures (g, ±ω) with constant scalar curvature is either Einstein, or the dual field of ω is Killing. Next, let (Mn , g) be a complete and connected Riemannian manifold of dimension at least 3 admitting a pair of Einstein-Weyl structures (g,±ω). Then the Einstein-Weyl vector field E (dual to the 1-form ω) generates an infinitesimal harmonic transformation if and only if E is Killing.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public