Wraith, David Surgery on Ricci positive manifolds. (English) Zbl 0915.53018 J. Reine Angew. Math. 501, 99-113 (1998). Let \(i\) is an isometric imbedding of the Riemannian product of a geodesic ball \(D^{m+1}\) in a round sphere \(S^m(N)\) with a round sphere \(S^{n-1}(r)\) into a Riemannian manifold \(M^{n+m}\) of positive Ricci curvature. Let \(T\) be a smooth map from \(S^{n-1}\) to \(SO(m+1)\), which induces a map \(T\) from \(D^{m+1}\times S^{n-1}\) to itself. In this paper, the author shows that, under certain conditions for \(N\) and \(r\), a metric of positive Ricci curvature can be chosen in \(D^{m+1}\times S^{n-1}\) such that a surgery on \(M\), using the trivialization \(T\circ i\), gives rise to a Riemannian manifold of positive Ricci curvature. Reviewer: M.Helena Noronha (Northridge) Cited in 2 ReviewsCited in 12 Documents MSC: 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 57R65 Surgery and handlebodies Keywords:Riemannian product; positive Ricci curvature; surgery PDFBibTeX XMLCite \textit{D. Wraith}, J. Reine Angew. Math. 501, 99--113 (1998; Zbl 0915.53018) Full Text: DOI Link