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Surgery on Ricci positive manifolds. (English) Zbl 0915.53018

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.

MSC:

53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
57R65 Surgery and handlebodies
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