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On Bach flat warped
product Einstein manifolds
Qiang Chen and Chenxu He |
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Vol. 265 (2013), No. 2, 313–326
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Abstract |
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We show that a compact warped product Einstein manifold with vanishing Bach tensor of dimension n ≥ 4 is either Einstein or a finite quotient of a warped product with an (n−1)-dimensional Einstein fiber. The fiber has constant curvature if n = 4. |
Keywords
warped product metric, Einstein manifold, Bach flat,
Bakry–Emery tensor
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Mathematical Subject Classification 2000
Primary: 53B20, 53C21, 53C25
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Milestones
Received: 5 July 2012
Revised: 3 December 2012
Accepted: 10 December 2012
Published: 28 August 2013
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Authors |
| Qiang Chen | |
| Department of Mathematics Lehigh University Bethlehem, PA 18015 United States |
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| Chenxu He | |
| Department of Mathematics Lehigh University Bethlehem, PA 18015 United States |
Department of Mathematics University of Oklahoma Norman, OK 73019 United States |
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