{"title":"复投影空间到四元投影空间的等调和映射","authors":"Isami Koga , Yasuyuki Nagatomo","doi":"10.1016/j.difgeo.2024.102167","DOIUrl":null,"url":null,"abstract":"<div><p>We classify equivariant harmonic maps of the complex projective spaces <span><math><mi>C</mi><msup><mrow><mi>P</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> into the quaternion projective spaces. To do this, we employ differential geometry of vector bundles and connections. When the domain is the complex projective <em>line</em>, we have one parameter family of those maps. (This result is already shown in <span>[2]</span> and <span>[4]</span> in other ways). However, when <span><math><mi>m</mi><mo>≧</mo><mn>2</mn></math></span>, we will obtain the rigidity results.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0926224524000603/pdfft?md5=50c3b21df49c5a546924763a29df2d65&pid=1-s2.0-S0926224524000603-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Equivariant harmonic maps of the complex projective spaces into the quaternion projective spaces\",\"authors\":\"Isami Koga , Yasuyuki Nagatomo\",\"doi\":\"10.1016/j.difgeo.2024.102167\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We classify equivariant harmonic maps of the complex projective spaces <span><math><mi>C</mi><msup><mrow><mi>P</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> into the quaternion projective spaces. To do this, we employ differential geometry of vector bundles and connections. When the domain is the complex projective <em>line</em>, we have one parameter family of those maps. (This result is already shown in <span>[2]</span> and <span>[4]</span> in other ways). However, when <span><math><mi>m</mi><mo>≧</mo><mn>2</mn></math></span>, we will obtain the rigidity results.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0926224524000603/pdfft?md5=50c3b21df49c5a546924763a29df2d65&pid=1-s2.0-S0926224524000603-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0926224524000603\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224524000603","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Equivariant harmonic maps of the complex projective spaces into the quaternion projective spaces
We classify equivariant harmonic maps of the complex projective spaces into the quaternion projective spaces. To do this, we employ differential geometry of vector bundles and connections. When the domain is the complex projective line, we have one parameter family of those maps. (This result is already shown in [2] and [4] in other ways). However, when , we will obtain the rigidity results.
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