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Rigidity results on gradient Schouten solitons
Romildo Pina, Ilton Menezes
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In this paper we consider ρ-Einstein solitons of type M= (Bⁿ, g^*) ×(Fᵐ,g_F), where (Bⁿ,g^*) is conformal to a pseudo-Euclidean space and invariant under the action of the pseudo-orthogonal group, and (Fᵐ,g_F) is an Einstein manifold. We provide all the solutions for the gradient Schouten soliton case. Moreover, in the Riemannian case, we prove that if M= (Bⁿ, g^*) ×(Fᵐ,g_F) is a complete gradient Schouten soliton then (Bⁿ,g^*) is isometric to 𝕊ⁿ⁻¹×ℝ and Fᵐ is a compact Einstein manifold.
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