Characterizations of Riemannian space forms, Einstein spaces and conformally flat spaces
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- by Bang-Yen Chen, Franki Dillen, Leopold Verstraelen and Luc Vrancken PDF
- Proc. Amer. Math. Soc. 128 (2000), 589-598 Request permission
Abstract:
In a recent paper the first author introduced two sequences of Riemannian invariants on a Riemannian manifold $M$, denoted respectively by $\delta (n_{1},\ldots ,n_{k})$ and $\hat \delta (n_{1},\ldots ,n_{k})$, which trivially satisfy $\delta (n_{1},\ldots ,n_{k})\geq \hat \delta (n_{1},\ldots ,n_{k})$. In this article, we completely determine the Riemannian manifolds satisfying the condition $\delta (n_{1},\ldots ,n_{k})=\hat \delta (n_{1},\ldots ,n_{k})$. By applying the notions of these $\delta$-invariants, we establish new characterizations of Einstein and conformally flat spaces; thus generalizing two well-known results of Singer-Thorpe and of Kulkarni.References
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Additional Information
- Bang-Yen Chen
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- MR Author ID: 193613
- Email: bychen@math.msu.edu
- Franki Dillen
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- Email: Franki.Dillen@wis.kuleuven.ac.be
- Leopold Verstraelen
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- MR Author ID: 178115
- Email: Leopold.Verstraelen@wis.kuleuven.ac.be
- Luc Vrancken
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- Email: Luc.Vrancken@wis.kuleuven.ac.be
- Received by editor(s): April 17, 1997
- Published electronically: July 23, 1999
- Additional Notes: The second and fourth authors were supported by a postdoctoral Fellow of the Fund for Scientific Research – Flanders (Belgium)(F.W.O.). Research supported by OT/TBA/95/9
- Communicated by: Christopher Croke
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 589-598
- MSC (1991): Primary 53B20; Secondary 53C42
- DOI: https://doi.org/10.1090/S0002-9939-99-05332-0
- MathSciNet review: 1664333