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On Ricci deformation
of a Riemannian metric on manifold with boundary
Ying Shen |
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Vol. 173 (1996), No. 1, 203–221
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Abstract |
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In this paper, we applied Hamilton’s Ricci flow to study the metric deformation on Riemannian manifolds with boundary. We proved a short time existence theorem for manifold with umbilical boundary. We also derived the Simons’ identity for the boundary under the Ricci flow. And as a corollary, we show that any three-manifold with totally geodesic boundary which admits positive Ricci curvature can be deformed to a space form with totally geodesic boundary. |
Mathematical Subject Classification 2000
Primary: 53C21
Secondary: 58G30
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Milestones
Received: 15 September 1993
Published: 1 March 1996
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Authors |
| Ying Shen | |
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