具有Killing - Ricci张量和Codazzi - Ricci张量的完备黎曼流形

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI:10.5922/0321-4796-2022-53-10

S. Stepanov, I. Tsyganok, J. Mikeš

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引用次数: 0

摘要

本文的目的是证明完全非紧黎曼流形上的Liouville型定理，即关于Killing - Ricci张量和Codazzi - Ricci张量不存在的定理。我们的结果补充了著名的贝塞关于爱因斯坦流形的专著最后一章中的两个经典消失定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.

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Differential Geometry of Manifolds of Figures

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