Some Solitons on Homogeneous Almost $\alpha$-Cosymplectic 3-Manifolds and Harmonic Manifolds

Abstract: We investigate the nature of Einstein solitons, whether it is steady, shrinking or expanding on almost alpha-cosymplectic 3-manifolds. We also prove that a simply connected homogeneous almost $\alpha$-cosymplectic 3-manifold, admitting a contact Einstein soliton, is an unimodular semidirect product Lie group. Finally, we show that a harmonic manifold admits a non-trivial Ricci soliton if and only if it is flat. Thus we show that rank one symmetric spaces of compact as well as non-compact type are stable under a Ricci soliton. In particular, we obtain a strengthening of Theorem 1 and Theorem 2 of the paper on the Stability of symmetric spaces of noncompact type under Ricci flow, by R. Balmer.

differential geometrysymplectic geometry

Audience: researchers in the topic

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Virtual seminar on geometry with symmetries

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