{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,9,30]],"date-time":"2022-09-30T04:36:27Z","timestamp":1664512587008},"reference-count":9,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,9,21]],"date-time":"2019-09-21T00:00:00Z","timestamp":1569024000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,9,21]],"date-time":"2019-09-21T00:00:00Z","timestamp":1569024000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s00454-019-00136-4","type":"journal-article","created":{"date-parts":[[2019,9,21]],"date-time":"2019-09-21T16:02:41Z","timestamp":1569081761000},"page":"575-589","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Centroaffine Duality for Spatial Polygons"],"prefix":"10.1007","volume":"66","author":[{"given":"Marcos","family":"Craizer","sequence":"first","affiliation":[]},{"given":"Sinesio","family":"Pesco","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,9,21]]},"reference":[{"key":"136_CR1","doi-asserted-by":"crossref","unstructured":"Arnold, V.: On the number of flattening points of space curves. In: Bunimovich, L.A., Gurevich, B.M., Pesin, Ya.B. (eds.) Sinai\u2019s Moscow Seminar on Dynamical Systems. American Mathematical Society Translations, vol. 171, pp. 11\u201322. American Mathematical Society, Providence (1996)","DOI":"10.1090\/trans2\/171\/02"},{"key":"136_CR2","unstructured":"Craizer, M., Garcia, R.A.: Umbilical centroaffine codimension 2 immersions and Loewner\u2019s type conjectures. (2018). arXiv:1811.07331"},{"key":"136_CR3","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/j.cagd.2017.06.001","volume":"57","author":"M Craizer","year":"2017","unstructured":"Craizer, M., Pesco, S.: Affine geometry of equal-volume polygons in $$3$$-space. Comput. Aided Geom. Des. 57, 44\u201356 (2017)","journal-title":"Comput. Aided Geom. Des."},{"issue":"3","key":"136_CR4","doi-asserted-by":"publisher","first-page":"580","DOI":"10.1007\/s00454-012-9448-y","volume":"48","author":"M Craizer","year":"2012","unstructured":"Craizer, M., Teixeira, R.C., da Silva, M.A.H.B.: Affine properties of convex equal-area polygons. Discrete Comput. Geom. 48(3), 580\u2013595 (2012)","journal-title":"Discrete Comput. Geom."},{"key":"136_CR5","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1017\/S0027763000004645","volume":"132","author":"K Nomizu","year":"1993","unstructured":"Nomizu, K., Sasaki, T.: Centroaffine immersions of codimension two and projective hypersurface theory. Nagoya Math. J. 132, 63\u201390 (1993)","journal-title":"Nagoya Math. J."},{"key":"136_CR6","unstructured":"Nomizu, K., Sasaki, T.: Affine Differential Geometry. Cambridge Tracts in Mathematics, vol. 111. Cambridge University Press, Cambridge (1994)"},{"key":"136_CR7","unstructured":"Pak, I.: Lectures on Discrete and Polyhedral Geometry (2010). http:\/\/www.math.ucla.edu\/~pak\/book.htm"},{"issue":"9","key":"136_CR8","doi-asserted-by":"publisher","first-page":"830","DOI":"10.1080\/00029890.2000.12005277","volume":"107","author":"S Tabachnikov","year":"2000","unstructured":"Tabachnikov, S.: A four vertex theorem for polygons. Am. Math. Monthly 107(9), 830\u2013833 (2000)","journal-title":"Am. Math. Monthly"},{"issue":"1\u20132","key":"136_CR9","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1007\/s00022-003-1641-y","volume":"77","author":"R Uribe-Vargas","year":"2003","unstructured":"Uribe-Vargas, R.: On $$4$$-flattening theorems and the curves of Carath\u00e9odory, Barner and Segre. J. Geom. 77(1\u20132), 184\u2013192 (2003)","journal-title":"J. Geom."}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00136-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-019-00136-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00136-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T06:48:35Z","timestamp":1664434115000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-019-00136-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,21]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["136"],"URL":"https:\/\/doi.org\/10.1007\/s00454-019-00136-4","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,9,21]]},"assertion":[{"value":"13 May 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 May 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 August 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 September 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}