Componentwise conformal vector fields on Riemannian almost product manifolds
نویسندگان
چکیده
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. M.S.C. 2010: 53C21, 53C15.
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