{"title":"几何平行的极脊空间和他们的线减少","authors":"K. Petelczyc, K. Prażmowski, M. Żynel","doi":"10.26493/1855-3974.2201.B65","DOIUrl":null,"url":null,"abstract":"The concept of spine geometry over a polar Grassmann space was introduced in [9]. The geometry in question belongs also to a wide family of partial affine line spaces. It is known that such a geometry -- e.g. the ``ordinary'' spine geometry, as considered in [13, 14] can be developed in terms of points, so called affine lines, and their parallelism (in this case this parallelism is not intrinsically definable: it is not `Veblenian', cf. [11]). This paper aims to prove an analogous result for polar spine spaces. As a by-product we obtain several other results on primitive notions for the geometry of polar spine spaces.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Geometry of the parallelism in polar spine spaces and their line reducts\",\"authors\":\"K. Petelczyc, K. Prażmowski, M. Żynel\",\"doi\":\"10.26493/1855-3974.2201.B65\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The concept of spine geometry over a polar Grassmann space was introduced in [9]. The geometry in question belongs also to a wide family of partial affine line spaces. It is known that such a geometry -- e.g. the ``ordinary'' spine geometry, as considered in [13, 14] can be developed in terms of points, so called affine lines, and their parallelism (in this case this parallelism is not intrinsically definable: it is not `Veblenian', cf. [11]). This paper aims to prove an analogous result for polar spine spaces. As a by-product we obtain several other results on primitive notions for the geometry of polar spine spaces.\",\"PeriodicalId\":8402,\"journal\":{\"name\":\"Ars Math. Contemp.\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-03-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ars Math. Contemp.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26493/1855-3974.2201.B65\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ars Math. Contemp.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26493/1855-3974.2201.B65","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Geometry of the parallelism in polar spine spaces and their line reducts
The concept of spine geometry over a polar Grassmann space was introduced in [9]. The geometry in question belongs also to a wide family of partial affine line spaces. It is known that such a geometry -- e.g. the ``ordinary'' spine geometry, as considered in [13, 14] can be developed in terms of points, so called affine lines, and their parallelism (in this case this parallelism is not intrinsically definable: it is not `Veblenian', cf. [11]). This paper aims to prove an analogous result for polar spine spaces. As a by-product we obtain several other results on primitive notions for the geometry of polar spine spaces.