{"title":"s ^6中的完全实曲面","authors":"Sharief Deshmukh","doi":"10.5556/J.TKJM.23.1992.4522","DOIUrl":null,"url":null,"abstract":"\n \n \nThe normal bundle $\\bar \\nu$ of a totally real surface $M$ in $S^6$ splits as $\\bar\\nu= JTM\\oplus \\bar\\mu$ where $TM$ is the tangent bundle of $M$ and $\\bar\\mu$ is subbundle of $\\bar\\nu$ which is invariant under the almost complex structure $J$. We study the totally real surfaces M of constant Gaussian curvature K for which the second fundamental form $h(x, y) \\in JTM$, and we show that $K = 1$ (that is, $M$ is totally geodesic). \n \n \n","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"117 1 1","pages":"11-14"},"PeriodicalIF":0.7000,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"TOTALLY REAL SURFACES IN $S^6$\",\"authors\":\"Sharief Deshmukh\",\"doi\":\"10.5556/J.TKJM.23.1992.4522\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n \\n \\nThe normal bundle $\\\\bar \\\\nu$ of a totally real surface $M$ in $S^6$ splits as $\\\\bar\\\\nu= JTM\\\\oplus \\\\bar\\\\mu$ where $TM$ is the tangent bundle of $M$ and $\\\\bar\\\\mu$ is subbundle of $\\\\bar\\\\nu$ which is invariant under the almost complex structure $J$. We study the totally real surfaces M of constant Gaussian curvature K for which the second fundamental form $h(x, y) \\\\in JTM$, and we show that $K = 1$ (that is, $M$ is totally geodesic). \\n \\n \\n\",\"PeriodicalId\":45776,\"journal\":{\"name\":\"Tamkang Journal of Mathematics\",\"volume\":\"117 1 1\",\"pages\":\"11-14\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tamkang Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5556/J.TKJM.23.1992.4522\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tamkang Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5556/J.TKJM.23.1992.4522","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
The normal bundle $\bar \nu$ of a totally real surface $M$ in $S^6$ splits as $\bar\nu= JTM\oplus \bar\mu$ where $TM$ is the tangent bundle of $M$ and $\bar\mu$ is subbundle of $\bar\nu$ which is invariant under the almost complex structure $J$. We study the totally real surfaces M of constant Gaussian curvature K for which the second fundamental form $h(x, y) \in JTM$, and we show that $K = 1$ (that is, $M$ is totally geodesic).
期刊介绍：
To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
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