Дифференциальная геометрия многообразий фигур (Jan 2023)

Pointwise orthogonal splitting of the space of TT-tensors

  • S. E. Stepanov,
  • I. I. Tsyganok

DOI
https://doi.org/10.5922/0321-4796-2023-54-2-4
Journal volume & issue
Vol. 54, no. 2
pp. 45 – 53

Abstract

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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