{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T22:29:09Z","timestamp":1760480949403},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Geom. Methods Mod. Phys."],"published-print":{"date-parts":[[2015,9]]},"abstract":"<jats:p> In this paper, we describe the geometry of the quaternionic Heisenberg groups from a Riemannian viewpoint. We show, in all dimensions, that they carry an almost 3-contact metric structure which allows us to define the metric connection that equips these groups with the structure of a naturally reductive homogeneous space. It turns out that this connection, which we shall call the canonical connection because of its analogy to the 3-Sasaki case, preserves the horizontal and vertical distributions and even the quaternionic contact (qc) structure of the quaternionic Heisenberg groups. We focus on the 7-dimensional case and prove that the canonical connection can also be obtained by means of a cocalibrated G<jats:sub>2<\/jats:sub> structure. We then study the spinorial properties of this group and present the noteworthy fact that it is the only known example of a manifold which carries generalized Killing spinors with three different eigenvalues. <\/jats:p>","DOI":"10.1142\/s0219887815600075","type":"journal-article","created":{"date-parts":[[2015,4,21]],"date-time":"2015-04-21T05:08:43Z","timestamp":1429592923000},"page":"1560007","source":"Crossref","is-referenced-by-count":7,"title":["Quaternionic Heisenberg groups as naturally reductive homogeneous spaces"],"prefix":"10.1142","volume":"12","author":[{"given":"Ilka","family":"Agricola","sequence":"first","affiliation":[{"name":"Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Stra\u00dfe, D-35032 Marburg, Germany"}]},{"given":"Ana Cristina","family":"Ferreira","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal"}]},{"given":"Reinier","family":"Storm","sequence":"additional","affiliation":[{"name":"Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Stra\u00dfe, D-35032 Marburg, Germany"}]}],"member":"219","published-online":{"date-parts":[[2015,9,23]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.difgeo.2014.11.005"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2013.05.001"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.geomphys.2009.10.003"},{"key":"rf6","volume":"265","author":"Biquard O.","year":"2000","journal-title":"Ast\u00e9risque"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3604-5"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S021988780600148X"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.5802\/aif.2203"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.4310\/AJM.2002.v6.n2.a5"},{"key":"rf11","volume":"1086","author":"Ivanov S.","year":"2014","journal-title":"Mem. Amer. Math. Soc."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdq061"},{"key":"rf13","series-title":"Wiley Classics Library","volume-title":"Foundations of Differential Geometry II","author":"Kobayashi S.","year":"1996"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/s10455-014-9415-3"},{"key":"rf15","first-page":"411","volume":"50","author":"Tricerri F.","year":"1993","journal-title":"Rend. Sem. Mat. Univ. Politec. Torino"}],"container-title":["International Journal of Geometric Methods in Modern Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219887815600075","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:16:07Z","timestamp":1565140567000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219887815600075"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9]]},"references-count":13,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2015,9,23]]},"published-print":{"date-parts":[[2015,9]]}},"alternative-id":["10.1142\/S0219887815600075"],"URL":"https:\/\/doi.org\/10.1142\/s0219887815600075","relation":{},"ISSN":["0219-8878","1793-6977"],"issn-type":[{"value":"0219-8878","type":"print"},{"value":"1793-6977","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9]]}}}