Isolation Theorems of the Bochner Curvature Type Tensors

Abstract

An isolation theorem of the Bochner curvature tensor of a Kähler-Einstein manifold is given, when its $L^{n/2}$-norm is small. Similarly an isolation theorem of the contact Bochner curvature tensor for a Sasakian manifold is obtained. Those theorems are derived from the Weitzenböck formula which gives non-linearity constraint on the Bochner curvature tensors.