{"id":5568,"date":"2020-02-05T08:29:08","date_gmt":"2020-02-05T08:29:08","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/ajb\/?p=5568"},"modified":"2020-02-05T08:29:08","modified_gmt":"2020-02-05T08:29:08","slug":"update-on-the-super-sasaki-metric-on-the-antitangent-bundle","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/ajb\/2020\/02\/05\/update-on-the-super-sasaki-metric-on-the-antitangent-bundle\/","title":{"rendered":"Update on “The super-Sasaki metric on the antitangent bundle”"},"content":{"rendered":"\n\n\n
\"board\"<\/td>\nThe short preprint
\nThe super-Sasaki metric on the antitangent bundle<\/a>, has now been extensivly rewriten and improved. I wrote about the first draft here<\/a>. <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

One of the major improvments is that I now clearly link the construction to almost Hermitian manifolds<\/a>, although the almost complex structure<\/a> plays no direct role in the lifting the metric<\/a> and almost sympletic structure<\/a> to the antitangent bundle. <\/p>\n

I now also give a concrete example of the super-Sasaki metric with Misner space<\/a> as the underlying pseudo-Riemannian manifold. As Misner space is topologically the infinite cylinder<\/a> it is canonically a symplectic manifold<\/a>. To my knowedge, the Riemannian metric I construct on the antitangent bundle of Misner space is completley new. <\/p>\n

I will briefly remark that Misner space has been used as a toy space-time to investigate various conjectures in general relativity<\/a> and semi-classical gravity<\/a>. This space has closed timelike curves<\/a>, known as CTCs, or to the layman, time machines. It was studying quantum fields on this space that led Hawking to his chronological protection conjecture<\/a>.<\/p>\n

There are, of course, lots of open questions here. It would be interesting to see how much of the classical theory of Sasaki carries over to this super-setting.<\/p>\n","protected":false},"excerpt":{"rendered":"

The short preprint The super-Sasaki metric on the antitangent bundle, has now been extensivly rewriten and improved. I wrote about the first draft here. One of the major improvments is that I now clearly link the construction to almost Hermitian manifolds, although the almost complex structure plays no direct role in the lifting the metric … Continue reading Update on “The super-Sasaki metric on the antitangent bundle”<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20,13],"tags":[],"class_list":["post-5568","post","type-post","status-publish","format-standard","hentry","category-post-doc-luxembourg","category-research-work"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/5568","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/comments?post=5568"}],"version-history":[{"count":7,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/5568\/revisions"}],"predecessor-version":[{"id":5575,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/5568\/revisions\/5575"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/media?parent=5568"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/categories?post=5568"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/tags?post=5568"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}