Asian Journal of Mathematics

Warped product Einstein metrics over spaces with constant scalar curvature

Chenxu He, Peter Petersen, and William Wylie

Full-text: Open access

Abstract

In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a product of Einstein manifolds. When the base is three dimensional and the dimension of the fiber is greater than one we show that the space is always rigid. We also exhibit examples of solvable four dimensional Lie groups that can be used as the base space of non-rigid warped product Einstein metrics showing that the result is not true in dimension greater than three. We also give some further natural curvature conditions that characterize the rigid examples in higher dimensions.

Article information

Source
Asian J. Math., Volume 18, Number 1 (2014), 159-190.

Dates
First available in Project Euclid: 27 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1409168518

Mathematical Reviews number (MathSciNet)
MR3215345

Zentralblatt MATH identifier
1292.53030

Subjects
Primary: 53B20: Local Riemannian geometry 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]

Keywords
Einstein manifolds warped products rigidity Ricci solitons solvable Lie groups

Citation

He, Chenxu; Petersen, Peter; Wylie, William. Warped product Einstein metrics over spaces with constant scalar curvature. Asian J. Math. 18 (2014), no. 1, 159--190. https://projecteuclid.org/euclid.ajm/1409168518


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