REMARKS ON COMPACT QUASI-EINSTEIN MANIFOLDS WITH BOUNDARY

In this paper, we prove that a compact quasi-Einstein manifold (M-n, g, u) of dimension n >= 4 with boundary partial derivative M, nonnegative sectional curvature and zero radial Weyl tensor is either isometric, up to scaling, to the standard hemisphere S-+(n), or g = dt(2) + psi(2)(t)g(L), and u = u(t), where g(L) is Einstein with nonnegative Ricci curvature. A similar classification result is obtained by assuming a fourth-order vanishing condition on the Weyl tensor. Moreover, a new example is presented in order to justify our assumptions. In addition, the case of dimension n = 3 is also discussed.

Automated summary

In this paper, the classification results of compact quasi-Einstein manifolds with boundary, nonnegative quasi-Einstein curvature, and zero radial Weyl tensor are proven. A new example is provided to justify the assumptions. The case of dimension 3 is also discussed.