Constant scalar curvature metrics on connected sums.
Joyce, Dominic (2003)
International Journal of Mathematics and Mathematical Sciences
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Joyce, Dominic (2003)
International Journal of Mathematics and Mathematical Sciences
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Jerry L. Kazdan (1981-1982)
Séminaire Bourbaki
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S.-T. Yau, R. Schoen (1988)
Inventiones mathematicae
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Akito Futaki (1993)
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Andrzej Derdziński (1988)
Bulletin de la Société Mathématique de France
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Sun-Yung A. Chang, Matthew J. Gursky, Paul C. Yang (2003)
Publications Mathématiques de l'IHÉS
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De, U.C., Ghosh, S.K. (2000)
Balkan Journal of Geometry and its Applications (BJGA)
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Graham Hall (2012)
Open Mathematics
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This paper discusses the connection between projective relatedness and conformal flatness for 4-dimensional manifolds admitting a metric of signature (+,+,+,+) or (+,+,+,−). It is shown that if one of the manifolds is conformally flat and not of the most general holonomy type for that signature then, in general, the connections of the manifolds involved are the same and the second manifold is also conformally flat. Counterexamples are provided which place limitations on the potential...
Peterson, Lawrence J. (ed.) (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Eric Boeckx, Lieven Vanhecke (2001)
Czechoslovak Mathematical Journal
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As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.