Abstract
AbstractSchouten tensor, which is expressed by the Ricci curvature and scalar curvature is a Codazzi tensor on a Riemannian manifold M(dimM>3)with harmonic Weyl conformal curvature tensor. By using this tensor, an operator r can be induced, which is self-adjoint relative to the L2 - inner product. Using this operator, some equalities and inequalities are obtained. Then by equalities between certain function on a compact local conformally symmetric Riemannie manifold, Einstein manifold and constant sectional curvature space are characterized. Some new theorems are established.KeywordsSelf-adjoint differential operatorconformally symmetric spaceSchouten tensor
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