Abstract
In this paper, for a compact manifold M with non-empty boundary \(\partial M\), we give a Koiso-type decomposition theorem, as well as an Ebin-type slice theorem, for the space of all Riemannian metrics on M endowed with a fixed conformal class on \(\partial M\). As a corollary, we give a characterization of relative Einstein metrics.
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Acknowledgements
I would like to thank my supervisor Kazuo Akutagawa for suggesting the initial direction for my study, his good advice and support. I would also like to thank the referee for suggesting that I arrange my notations and cite some previous related works.
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Communicated by S. A. Chang.
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Hamanaka, S. Decompositions of the space of Riemannian metrics on a compact manifold with boundary. Calc. Var. 60, 194 (2021). https://doi.org/10.1007/s00526-021-02070-x
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DOI: https://doi.org/10.1007/s00526-021-02070-x