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Mar 30, 2011 at 20:48 comment added Joseph O'Rourke @Willie: My oversight!
Mar 30, 2011 at 16:48 comment added Willie Wong To add to Anton's comment: the Riemannian Schwarzschild metrics form another one-parameter family of Ricci-flat that are not (locally) conformally isometric to each other, are you sure you want them to have distance zero between them? If you want the motivation from the Ricci flow, wouldn't it make more sense to actually consider the energy functional used there? terrytao.wordpress.com/2008/04/24/…
Mar 30, 2011 at 16:11 comment added Willie Wong @Joseph: considering the OP's earlier question mathoverflow.net/questions/59715/… I daresay he is somewhat familiar with the Willmore functional.
Mar 30, 2011 at 15:47 comment added Anton Petrunin So, any one parameter family of flat tori has zero energy... Are you sure you want it this way?
Mar 30, 2011 at 15:38 comment added Joseph O'Rourke This earlier MO question is perhaps tangentially relevant: "Measures of the complexity of a metric" mathoverflow.net/questions/32527 . See especially Will Jagy's discussion of the Willmore functional.
Mar 30, 2011 at 15:00 history asked bobye CC BY-SA 2.5