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Differential Geometry of Manifolds

2023 №54(2)

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Stepanov S.E. Tsyganok I.I.

Pointwise orthogonal splitting of the space of TT-tensors

DOI
10.5922/0321-4796-2023-54-2-4
Pages
45-53
Riemannian manifold TT-tensor Liouville-type non-exis­ten­ce theorems sectional curvature

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.

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