Korean J. Math. Vol. 34 No. 1 (2026) pp.83-94
DOI: https://doi.org/10.11568/kjm.2026.34.1.83

Einstein-like warped product manifolds which are not Einstein

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Published: Mar 30, 2026
Keywords:
Einstein manifold, warped product manifold, Einstein-like manifold
Mathematics Subject Classification:
34C40, 53C25

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Keisuke Ueno
Department of Mathematical Sciences Faculty of Science, Yamagata University, Yamagata, Japan

Abstract

In this paper, we firstly present a necessary and sufficient condition for a warped product manifold to be an Einstein-like manifold. By using this condition, we prove that if a warping function is not constant, then the fiber space of an Einstein-like warped product manifold is an Einstein manifold. Moreover we construct new examples of Einstein-like manifold which are not Einstein.



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