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- Title
Componentwise conformal vector fields on Riemannian almost product manifolds.
- Authors
Ortega, M.; Palomo, F. J.; Romero, A.
- Abstract
On a Riemannian almost product manifold, the notion of a componentwise conformal vector field is introduced and several examples are exhibited. We show that this class of vector fields is a conformal invariant. For a compact manifold, a Bochner type integral formula for the Ricci tensor on such vector fields is obtained. Then, integral inequalities which link a curvature condition with the existence of componentwise conformal vector fields are obtained. Also, applications to Riemaniann submersions are given, obtaining a new characterization of the standard flat n-torus.
- Subjects
CONFORMAL field theory; VECTOR fields; RIEMANNIAN manifolds; MATHEMATICAL formulas; SUBMERSIONS (Mathematics)
- Publication
Balkan Journal of Geometry & Its Applications, 2014, Vol 19, Issue 1, p88
- ISSN
1224-2780
- Publication type
Article