Proceedings of the Japan Academy, Series A, Mathematical Sciences

On conformally flat critical Riemannian metrics for a curvature functional

Minyo Katagiri

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Abstract

The normalized $L^2$-norm of the traceless part of the Ricci curvature defines a Riemannian functional on the space of Riemannian metrics. In this paper, we will consider the critical Riemannian metrics with a flat conformal structure for this functional.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 2 (2005), 27-29.

Dates
First available in Project Euclid: 18 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1116442056

Digital Object Identifier
doi:10.3792/pjaa.81.27

Mathematical Reviews number (MathSciNet)
MR2126073

Zentralblatt MATH identifier
1094.58007

Subjects
Primary: 58E11: Critical metrics
Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords
Critical Riemannian metrics Riemannian functionals

Citation

Katagiri, Minyo. On conformally flat critical Riemannian metrics for a curvature functional. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 2, 27--29. doi:10.3792/pjaa.81.27. https://projecteuclid.org/euclid.pja/1116442056


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References

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