In this paper we construct constant scalar curvature metrics on the generalized connected sum of two compact Riemannian manifolds (M_1,g_1) and (M_2,g_2) along a common Riemannian submanifold (K,g_K), in the case where the codimension of K is at least 3 and the manifolds M_1 and M_2 have the same nonzero constant scalar curvature S. This yields a generalization of the Joyce’s results for point-wise connected sums.
Generalized connected sum construction for nonzero constant scalar curvature metrics
MAZZIERI, LORENZO
2008
Abstract
In this paper we construct constant scalar curvature metrics on the generalized connected sum of two compact Riemannian manifolds (M_1,g_1) and (M_2,g_2) along a common Riemannian submanifold (K,g_K), in the case where the codimension of K is at least 3 and the manifolds M_1 and M_2 have the same nonzero constant scalar curvature S. This yields a generalization of the Joyce’s results for point-wise connected sums.File in questo prodotto:
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Generalized connected sum construction for nonzero CSC metrics.pdf
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