Multiply warped products with compact Einstein manifolds

Abstract

We study multiply warped products with compact Einstein manifolds. We obtain that there does not exist connected, compact Einstein multiply warped products if the scalar curvature is non-positive. It is also found that there does not exist non-trivial connected Einstein multiply warped product manifolds with compact base or compact fibres.

Mathematics Subject Classification (2010):

• 53C25
• 53C50
• 53B20

Key words:

• Multiply warped product manifold
• compact manifold
• Einstein manifold