A remark on Einstein warped products

Abstract

We prove triviality results for Einstein warped products with non-compact bases. These extend previous work by D.-S. Kim and Y.-H. Kim. The proof, from the viewpoint of "quasi-Einstein manifolds" introduced by J. Case, Y.-S. Shu and G. Wei, rely on maximum principles at infinity and Liouville-type theorems.

12 pages. Corrected typos. Final version: to appear on Pacific J. Math

References in corpus (2)

• On the nonexistence of quasi-Einstein metrics
• Myers' type theorems and some related oscillation results

Cited by in corpus (4)

• Gradient Ricci almost soliton warped product
• A note on gradient Ricci soliton warped metrics
• Some triviality results for quasi-Einstein manifolds and Einstein warped products
• Gradient Einstein-type warped products: rigidity, existence and nonexistence results via a nonlinear PDE