{"title":"凸域上的复测地线与半管域上的复测地线","authors":"Sylwester Zając, Paweł Zapałowski","doi":"10.1515/advgeom-2020-0009","DOIUrl":null,"url":null,"abstract":"Abstract In this paper the complex geodesics of a convex domain in ℂn are studied. One of the main results provides a certain necessary condition for a holomorphic map to be a complex geodesic for a convex domain in ℂn. The established condition is of geometric nature and it allows to find a formula for every complex geodesic. The ℂ-convexity of semitube domains is also discussed.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/advgeom-2020-0009","citationCount":"0","resultStr":"{\"title\":\"Complex geodesics in convex domains and ℂ-convexity of semitube domains\",\"authors\":\"Sylwester Zając, Paweł Zapałowski\",\"doi\":\"10.1515/advgeom-2020-0009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper the complex geodesics of a convex domain in ℂn are studied. One of the main results provides a certain necessary condition for a holomorphic map to be a complex geodesic for a convex domain in ℂn. The established condition is of geometric nature and it allows to find a formula for every complex geodesic. The ℂ-convexity of semitube domains is also discussed.\",\"PeriodicalId\":7335,\"journal\":{\"name\":\"Advances in Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/advgeom-2020-0009\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/advgeom-2020-0009\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/advgeom-2020-0009","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Complex geodesics in convex domains and ℂ-convexity of semitube domains
Abstract In this paper the complex geodesics of a convex domain in ℂn are studied. One of the main results provides a certain necessary condition for a holomorphic map to be a complex geodesic for a convex domain in ℂn. The established condition is of geometric nature and it allows to find a formula for every complex geodesic. The ℂ-convexity of semitube domains is also discussed.
期刊介绍：
Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.
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