On the classification of noncompact steady quasi-Einstein manifold with vanishing condition on the Weyl tensor

H. Baltazar; M. Matos Neto

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arXiv · 1709.07280

On the classification of noncompact steady quasi-Einstein manifold with vanishing condition on the Weyl tensor

H. Baltazar·M. Matos Neto

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Abstract

The aim of this paper is to study complete (noncompact) steady $m$-quasi-Einstein manifolds satisfying a fourth-order vanishing condition on the Weyl tensor. In this case, we are able to prove that a steady $m$-quasi-Einstein manifold ($m>1$) on a simply connected $n$-dimensional manifold $(M^{n},g)$, $(n\geq4),$ with nonnegative Ricci curvature and zero radial Weyl curvature must be a warped product with $(n-1)-$dimensional Einstein fiber, provided that $M$ has fourth order divergence-free Weyl tensor (i.e., ${\rm div}^{4}W=0$).

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BibTeX RIS

H. Baltazar, M. Matos Neto. 2017-09-21. On the classification of noncompact steady quasi-Einstein manifold with vanishing condition on the Weyl tensor. https://arxiv.org/abs/1709.07280

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