Corrigendum to “The pluriclosed flow for T^{2}-invariant Vaisman metrics on the Kodaira-Thurston surface” [J. Geom. Phys. 201 (2024) 105197] (S0393044024000986), (10.1016/j.geomphys.2024.105197)
Other Scholarly Work
Fino, A, Grantcharov, G, Perez, E. (2024). Corrigendum to “The pluriclosed flow for T^{2}-invariant Vaisman metrics on the Kodaira-Thurston surface” [J. Geom. Phys. 201 (2024) 105197] (S0393044024000986), (10.1016/j.geomphys.2024.105197)
. JOURNAL OF GEOMETRY AND PHYSICS, 203 10.1016/j.geomphys.2024.105254
Fino, A, Grantcharov, G, Perez, E. (2024). Corrigendum to “The pluriclosed flow for T^{2}-invariant Vaisman metrics on the Kodaira-Thurston surface” [J. Geom. Phys. 201 (2024) 105197] (S0393044024000986), (10.1016/j.geomphys.2024.105197)
. JOURNAL OF GEOMETRY AND PHYSICS, 203 10.1016/j.geomphys.2024.105254
The authors would like to thank Freid Tong [1] for pointing out that Theorem 3.2 holds only under the extra assumption that the initial metric has constant scalar curvature. As a consequence Theorem 3.2 needs to be changed to Theorem 3.2 Let [Formula presented.] be the fundamental form of a [Formula presented.]-invariant Vaisman metric on the Kodaira-Thurston surface M. Then the pluriclosed flow starting with [Formula presented.] preserves the Vaisman condition if and only if [Formula presented.] has constant scalar curvature. At the end of the proof of Theorem 3.2 one needs to add the following: [Formula presented.] and [Formula presented.] remain constant along the flow if and only if [Formula presented.] is constant along the flow or equivalently if and only if [Formula presented.] has constant scalar curvature. The abstract also has to be changed to: Abstract In this note we study [Formula presented.]-invariant pluriclosed metrics on the Kodaira-Thurston surface. We obtain a characterization of [Formula presented.]-invariant Vaisman metrics, and notice that the Kodaira-Thurston surface admits Vaisman metrics with non-constant scalar curvature. Then we study the behavior of the Vaisman condition in relation to the pluriclosed flow. As a consequence, we show that the pluriclosed flow preserves the Vaisman condition if and only if the initial [Formula presented.]-invariant Vaisman metric has constant scalar curvature. Moreover, the last sentence of the Introduction at page 2 has to be changed to: Then, as a main result we prove that if [Formula presented.] is the fundamental form of a [Formula presented.]-invariant Vaisman metric on the Kodaira-Thurston surface then the pluriclosed flow starting with [Formula presented.] preserves the Vaisman condition if and only if the scalar curvature is constant. As a result, the pluriclosed flow in the example after Theorem 3.2 does not preserve the Vaisman condition. The authors would like to apologize for any inconvenience caused.