{"title":"Minkowski 3-空间中的类时间W曲面","authors":"N. Alluhaibi, R. Abdel-Baky","doi":"10.1155/2022/7998748","DOIUrl":null,"url":null,"abstract":"<jats:p>Let <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <mi>M</mi>\n </math>\n </jats:inline-formula> and <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\n <msup>\n <mrow>\n <mi>M</mi>\n </mrow>\n <mrow>\n <mo>∗</mo>\n </mrow>\n </msup>\n </math>\n </jats:inline-formula> be two timelike surfaces in Minkowski 3-space <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\n <msubsup>\n <mrow>\n <mi>ℝ</mi>\n </mrow>\n <mrow>\n <mn>1</mn>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msubsup>\n </math>\n </jats:inline-formula>. If there exists a spacelike (timelike) Darboux line congruence between each point of <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\n <mi>M</mi>\n </math>\n </jats:inline-formula> and <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\n <msup>\n <mrow>\n <mi>M</mi>\n </mrow>\n <mrow>\n <mo>∗</mo>\n </mrow>\n </msup>\n </math>\n </jats:inline-formula>, then the surfaces are timelike Weingarten surfaces. It turns out their Tschebyscheff angles are solutions of the Sinh-Gordon equation, and the surfaces are related to each other by Backlund’s transformation. Finally, a method to construct new timelike Weingarten surface has been found.</jats:p>","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Timelike <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M1\\\">\\n <mi>W</mi>\\n </math>-Surfaces in Minkowski 3-Space <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M2\\\">\\n <msubsup>\\n <mrow>\\n \",\"authors\":\"N. Alluhaibi, R. Abdel-Baky\",\"doi\":\"10.1155/2022/7998748\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<jats:p>Let <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M3\\\">\\n <mi>M</mi>\\n </math>\\n </jats:inline-formula> and <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M4\\\">\\n <msup>\\n <mrow>\\n <mi>M</mi>\\n </mrow>\\n <mrow>\\n <mo>∗</mo>\\n </mrow>\\n </msup>\\n </math>\\n </jats:inline-formula> be two timelike surfaces in Minkowski 3-space <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M5\\\">\\n <msubsup>\\n <mrow>\\n <mi>ℝ</mi>\\n </mrow>\\n <mrow>\\n <mn>1</mn>\\n </mrow>\\n <mrow>\\n <mn>3</mn>\\n </mrow>\\n </msubsup>\\n </math>\\n </jats:inline-formula>. If there exists a spacelike (timelike) Darboux line congruence between each point of <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M6\\\">\\n <mi>M</mi>\\n </math>\\n </jats:inline-formula> and <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M7\\\">\\n <msup>\\n <mrow>\\n <mi>M</mi>\\n </mrow>\\n <mrow>\\n <mo>∗</mo>\\n </mrow>\\n </msup>\\n </math>\\n </jats:inline-formula>, then the surfaces are timelike Weingarten surfaces. It turns out their Tschebyscheff angles are solutions of the Sinh-Gordon equation, and the surfaces are related to each other by Backlund’s transformation. Finally, a method to construct new timelike Weingarten surface has been found.</jats:p>\",\"PeriodicalId\":49251,\"journal\":{\"name\":\"Journal of Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2022-03-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2022/7998748\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2022/7998748","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Let and be two timelike surfaces in Minkowski 3-space . If there exists a spacelike (timelike) Darboux line congruence between each point of and , then the surfaces are timelike Weingarten surfaces. It turns out their Tschebyscheff angles are solutions of the Sinh-Gordon equation, and the surfaces are related to each other by Backlund’s transformation. Finally, a method to construct new timelike Weingarten surface has been found.
期刊介绍：
Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics.
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