• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.471-478
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• 2024

The aim of this paper is to investigate some properties of the critical points equations on the statistical manifolds. We obtain some geometric equations on the statistical manifolds which admit critical point equations. We give a relation only between potential function and difference tensor for a CPE metric on the statistical manifolds to be Einstein.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.117-123
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• 2004

It has been conjectured that, on a compact orient able manifold M, a critical point of the total scalar curvature functional restricted the space of unit volume metrics of constant scalar curvature is Einstein. In this paper we show that if a manifold is a 3-dimensional warped product, then (M, g) cannot be a critical point unless it is isometric to the standard sphere.