Geodesics without conjugate points and curvatures at infinity
We study the asymptotic behavior of curvature and prove that the integral of curvature along a geodesic without conjugate points is nonpositive and some generalizations of Myers theorem and Cohn-Vossen's theorem. Some applications are also given.
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| Format: | Article |
| Language: | English |
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Academia Brasileira de Ciências
2000-01-01
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| Series: | Anais da Academia Brasileira de Ciências |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652000000200002 |
| _version_ | 1818909333083127808 |
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| author | MENDONÇA SÉRGIO ZHOU DETANG |
| author_facet | MENDONÇA SÉRGIO ZHOU DETANG |
| author_sort | MENDONÇA SÉRGIO |
| collection | DOAJ |
| description | We study the asymptotic behavior of curvature and prove that the integral of curvature along a geodesic without conjugate points is nonpositive and some generalizations of Myers theorem and Cohn-Vossen's theorem. Some applications are also given. |
| first_indexed | 2024-12-19T22:25:14Z |
| format | Article |
| id | doaj.art-3521171818304db1b0cd1d66218c22d0 |
| institution | Directory Open Access Journal |
| issn | 0001-3765 1678-2690 |
| language | English |
| last_indexed | 2024-12-19T22:25:14Z |
| publishDate | 2000-01-01 |
| publisher | Academia Brasileira de Ciências |
| record_format | Article |
| series | Anais da Academia Brasileira de Ciências |
| spelling | doaj.art-3521171818304db1b0cd1d66218c22d02022-12-21T20:03:31ZengAcademia Brasileira de CiênciasAnais da Academia Brasileira de Ciências0001-37651678-26902000-01-01722117124Geodesics without conjugate points and curvatures at infinityMENDONÇA SÉRGIOZHOU DETANGWe study the asymptotic behavior of curvature and prove that the integral of curvature along a geodesic without conjugate points is nonpositive and some generalizations of Myers theorem and Cohn-Vossen's theorem. Some applications are also given.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652000000200002Riemannian manifoldgeodesicconjugate point |
| spellingShingle | MENDONÇA SÉRGIO ZHOU DETANG Geodesics without conjugate points and curvatures at infinity Anais da Academia Brasileira de Ciências Riemannian manifold geodesic conjugate point |
| title | Geodesics without conjugate points and curvatures at infinity |
| title_full | Geodesics without conjugate points and curvatures at infinity |
| title_fullStr | Geodesics without conjugate points and curvatures at infinity |
| title_full_unstemmed | Geodesics without conjugate points and curvatures at infinity |
| title_short | Geodesics without conjugate points and curvatures at infinity |
| title_sort | geodesics without conjugate points and curvatures at infinity |
| topic | Riemannian manifold geodesic conjugate point |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652000000200002 |
| work_keys_str_mv | AT mendoncasergio geodesicswithoutconjugatepointsandcurvaturesatinfinity AT zhoudetang geodesicswithoutconjugatepointsandcurvaturesatinfinity |