Abstract
Bach-flat metrics were introduced in the study of a conformally invariant gravitational theory and has played important roles in general relativity and geometry. This metric is the most natural generalization of an Einstein metric.
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References
A. Ache, J. Viaclovsky, Obstruction-flat asymptotically locally Euclidean metrics. Geom. Funct. Anal. 22, 832–877 (2012)
A.L. Besse, Einstein Manifolds (Springer, Berlin, 1987)
S.Y.A. Chang, M. Gursky, P. Yang, A conformally invariant Sphere theorem in four dimension. Publ. Math. IHES. 98, 105–143 (2003)
S.Y.A. Chang, J. Qing, P. Yang, On a conformal gap and finiteness theorem for a class of four manifolds. Geom. Funct. Anal. 17, 404–434 (2007)
R. Hamilton, Three-manifolds with positive Ricci curvature. J. Differ. Geom. 17, 255–306 (1982)
S. Kim, Zero scalar curvature on open manifolds. Commun. Korean Math. Soc. 13, 539–544 (1998)
S. Kim, Rigidity of noncompact complete Bach-flat manifolds. J. Geom. Phys. 60, 637–642 (2010)
J. Streets, Asymptotic curvature decay and removal of singularities of Bach-flat metrics. Trans. Am. Math. Soc. 362, 1301–1324 (2010)
G. Tian, J. Viaclovsky, Bach-flat asymptotically locally Euclidean metrics. Invent. Math. 160, 357–415 (2005)
Acknowledgements
This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (2011-0025674).
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Kim, S. (2015). Rigidity of Bach-Flat Manifolds. In: González, M., Yang, P., Gambino, N., Kock, J. (eds) Extended Abstracts Fall 2013. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-21284-5_7
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DOI: https://doi.org/10.1007/978-3-319-21284-5_7
Publisher Name: Birkhäuser, Cham
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