{"title":"黎曼流形中的切轨迹","authors":"K. Hatsuse, Y. Morita","doi":"10.5036/BFSIU1968.18.45","DOIUrl":null,"url":null,"abstract":"We assume hereafter M satisfies the condition (B) at p, and assume sectional curvatures Kσ of M are bounded from below. Let i(p) be the injective radius at p, and let i(M) the injective radius of M. Then we can choose a Riemannian metric g on M as i(M)=1. We denote by L(γ) the length of a piecewise smooth curve γ. Let δ be a lower bound for sectional curvatures Kσ. Let K0=min {δ,0} and N(K0) a simply connected complete Riemannian manifold of constant sectional curvature K0. We consider a geodesic triangle abc in N(K0) which consists of","PeriodicalId":141145,"journal":{"name":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1986-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Cut locus in a Riemannian manifold\",\"authors\":\"K. Hatsuse, Y. Morita\",\"doi\":\"10.5036/BFSIU1968.18.45\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We assume hereafter M satisfies the condition (B) at p, and assume sectional curvatures Kσ of M are bounded from below. Let i(p) be the injective radius at p, and let i(M) the injective radius of M. Then we can choose a Riemannian metric g on M as i(M)=1. We denote by L(γ) the length of a piecewise smooth curve γ. Let δ be a lower bound for sectional curvatures Kσ. Let K0=min {δ,0} and N(K0) a simply connected complete Riemannian manifold of constant sectional curvature K0. We consider a geodesic triangle abc in N(K0) which consists of\",\"PeriodicalId\":141145,\"journal\":{\"name\":\"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics\",\"volume\":\"24 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1986-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5036/BFSIU1968.18.45\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/BFSIU1968.18.45","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We assume hereafter M satisfies the condition (B) at p, and assume sectional curvatures Kσ of M are bounded from below. Let i(p) be the injective radius at p, and let i(M) the injective radius of M. Then we can choose a Riemannian metric g on M as i(M)=1. We denote by L(γ) the length of a piecewise smooth curve γ. Let δ be a lower bound for sectional curvatures Kσ. Let K0=min {δ,0} and N(K0) a simply connected complete Riemannian manifold of constant sectional curvature K0. We consider a geodesic triangle abc in N(K0) which consists of
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