{"title":"具有弱横向kill算子的非平坦复空间形式的实超曲面","authors":"Zejun Hu, Xi Zhang","doi":"10.1016/j.difgeo.2023.102061","DOIUrl":null,"url":null,"abstract":"<div><p>Wang and Zhang in (2022) <span>[20]</span> and (2023) <span>[21]</span> characterized type (A) real hypersurfaces of the nonflat complex space forms as having transversal Killing structure Lie operator <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>ξ</mi></mrow></msub></math></span> or contact Lie operator <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>ξ</mi></mrow></msub><mi>ϕ</mi></math></span>. In this note, we extend the above results by showing that the class of real hypersurfaces of type (A), (B) and the ruled real hypersurfaces in the nonflat complex space forms are locally characterized by having weakly transversal Killing operator <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>ξ</mi></mrow></msub></math></span> or <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>ξ</mi></mrow></msub><mi>ϕ</mi></math></span>.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Real hypersurfaces of nonflat complex space forms with weakly transversal Killing operators\",\"authors\":\"Zejun Hu, Xi Zhang\",\"doi\":\"10.1016/j.difgeo.2023.102061\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Wang and Zhang in (2022) <span>[20]</span> and (2023) <span>[21]</span> characterized type (A) real hypersurfaces of the nonflat complex space forms as having transversal Killing structure Lie operator <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>ξ</mi></mrow></msub></math></span> or contact Lie operator <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>ξ</mi></mrow></msub><mi>ϕ</mi></math></span>. In this note, we extend the above results by showing that the class of real hypersurfaces of type (A), (B) and the ruled real hypersurfaces in the nonflat complex space forms are locally characterized by having weakly transversal Killing operator <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>ξ</mi></mrow></msub></math></span> or <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>ξ</mi></mrow></msub><mi>ϕ</mi></math></span>.</p></div>\",\"PeriodicalId\":51010,\"journal\":{\"name\":\"Differential Geometry and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Geometry and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0926224523000876\",\"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":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224523000876","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Real hypersurfaces of nonflat complex space forms with weakly transversal Killing operators
Wang and Zhang in (2022) [20] and (2023) [21] characterized type (A) real hypersurfaces of the nonflat complex space forms as having transversal Killing structure Lie operator or contact Lie operator . In this note, we extend the above results by showing that the class of real hypersurfaces of type (A), (B) and the ruled real hypersurfaces in the nonflat complex space forms are locally characterized by having weakly transversal Killing operator or .
期刊介绍:
Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.