Дифференциальная геометрия многообразий фигур (Nov 2022)

Complete Riemannian manifolds with Killing — Ricci and Codazzi — Ricci tensors

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

DOI
https://doi.org/10.5922/0321-4796-2022-53-10
Journal volume & issue
no. 53
pp. 112 – 117

Abstract

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The purpose of this paper is to prove of Liouville type theorems, i. e., theorems on the non-existence of Killing — Ric­ci and Codazzi — Ricci tensors on complete non-com­pact Riemannian manifolds. Our results complement the two classical vanishing theorems from the last chapter of fa­mous Besse’s monograph on Einstein manifolds.

Keywords