Geodesic
K-stable smooth Fano threefolds of Picard rank two
Forum of Mathematics, Sigma, Tome 12 (2024)

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We prove that all smooth Fano threefolds in the families and are K-stable, and we also prove that smooth Fano threefolds in the family that satisfy one very explicit generality condition are K-stable. 
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     author = {Ivan Cheltsov and Elena Denisova and Kento Fujita},
     title = {K-stable smooth {Fano} threefolds of {Picard} rank two},
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Ivan Cheltsov; Elena Denisova; Kento Fujita. K-stable smooth Fano threefolds of Picard rank two. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.5

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