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Characterizations of Riemannian Space Forms, Einstein Spaces and Conformally Flat Spaces
Bang-Yen Chen, Franki Dillen, Leopold Verstraelen and Luc Vrancken
Proceedings of the American Mathematical Society
Vol. 128, No. 2 (Feb., 2000), pp. 589-598
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/119926
Page Count: 10
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In a recent paper the first author introduced two sequences of Riemannian invariants on a Riemannian manifold M, denoted respectively by δ (n1,...,nk) and δ̂(n1,...,nk), which trivially satisfy δ (n1,...,nk)≥ δ̂(n1,...,nk). In this article, we completely determine the Riemannian manifolds satisfying the condition δ (n1,...,nk)=δ̂(n1,...,nk). By applying the notions of these δ -invariants, we establish new characterizations of Einstein and conformally flat spaces; thus generalizing two well-known results of Singer-Thorpe and Kulkarni.
Proceedings of the American Mathematical Society © 2000 American Mathematical Society