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Title: On Uniqueness Theoremsfor Ricci Tensor (English)
Author: Khripunova, Marina B.
Author: Stepanov, Sergey E.
Author: Tsyganok, Irina I.
Author: Mikeš, Josef
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 55
Issue: 1
Year: 2016
Pages: 47-52
Summary lang: English
Category: math
Summary: In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold $M$ and a symmetric 2-tensor $r$, construct a metric on $M$ whose Ricci tensor equals $r$. In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with non-negative section curvature. In addition, we extended our result to complete non-compact Riemannian manifolds with nonnegative sectional curvature and with finite total scalar curvature. (English)
Keyword: Uniqueness theorem for Ricci tensor
Keyword: compact and complete Riemannian manifolds
Keyword: vanishing theorem
MSC: 53C20
idZBL: Zbl 1373.53045
idMR: MR3674599
Date available: 2016-08-30T11:53:27Z
Last updated: 2018-01-10
Stable URL:
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