Pointwise orthogonal splitting of the space of TT-tensors

Abstract

In the present paper we consider pointwise orthogonal split­ting of the space of well-known TT-tensors on Rieman­nian manifolds. Tensors of the first subspace belong to the ker­nel of the Bourguignon Laplacian, and the tensors of the se­cond subspace belong to the kernel of the Sampson Lap­la­cian. We give examples and prove Liouville-type non-exis­tence theorems of these tensors.

Keywords

• riemannian manifold
• tt-tensor
• liouville-type non-exis­ten­ce theorems
• sectional curvature