{"created":"2022-01-28T01:58:15.701010+00:00","id":2006999,"links":{},"metadata":{"_buckets":{"deposit":"da5d0898-7c4a-486f-a189-8ea84e0e4d4a"},"_deposit":{"id":"2006999","owners":[1],"pid":{"revision_id":0,"type":"depid","value":"2006999"},"status":"published"},"_oai":{"id":"oai:u-ryukyu.repo.nii.ac.jp:02006999","sets":["1642837622505:1642837628262:1642837638076","1642838403551:1642838406414"]},"author_link":[],"item_1617186331708":{"attribute_name":"Title","attribute_value_mlt":[{"subitem_1551255647225":"COMPUTER-AIDED VERIFICATION OF THE GAUSS-BONNET FORMULA FOR CLOSED SURFACES","subitem_1551255648112":"en"}]},"item_1617186419668":{"attribute_name":"Creator","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Kamiyama, Yasuhiko","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"神山, 靖彦","creatorNameLang":"ja"}]}]},"item_1617186476635":{"attribute_name":"Access Rights","attribute_value_mlt":[{"subitem_1522299639480":"open access","subitem_1600958577026":"http://purl.org/coar/access_right/c_abf2"}]},"item_1617186626617":{"attribute_name":"Description","attribute_value_mlt":[{"subitem_description":"If X, a compact connected closed C^∞-surface with Euler-Poincaré characteristic _X(X), has a Riemannian metric, and if K : X → R is the Gauss-curvature and dV is the absolute value of the exterior 2-form which represents the volume, then according to the theorem of Gauss-Bonnet, which holds for orientable as well as non-orientable surfaces, (2π)/1 ∫_xKdV=_X(X). When X is the standard sphere or torus in R^3 , the Gaussian curvature is well-known and we can compute the left-hand side explicitly. Let X be a compact connected closed C^∞-surface of any genus. In this paper, we construct an embedding of X into R^3 or R^4 according as X is orientable or nonorientable. We equip X with the Riemannian metric as a Riemannian submanifold of R^3 or R^4. Then, with the aid of a computer, we compute the left-hand side numerically for the cases that the genus of X is small. The computer data are sufficiently nice and coincide with the right-hand side without errors. Such nice data are obtained by converting double integrals to infinite integrals.","subitem_description_type":"Other"},{"subitem_description":"紀要論文","subitem_description_type":"Other"}]},"item_1617186643794":{"attribute_name":"Publisher","attribute_value_mlt":[{"subitem_1522300295150":"en","subitem_1522300316516":"Department of Mathematical Science, Faculty of Science, University of the Ryukyus"}]},"item_1617186702042":{"attribute_name":"Language","attribute_value_mlt":[{"subitem_1551255818386":"eng"}]},"item_1617186783814":{"attribute_name":"Identifier","attribute_value_mlt":[{"subitem_identifier_type":"HDL","subitem_identifier_uri":"http://hdl.handle.net/20.500.12000/23589"}]},"item_1617186920753":{"attribute_name":"Source Identifier","attribute_value_mlt":[{"subitem_1522646500366":"ISSN","subitem_1522646572813":"1344-008X"},{"subitem_1522646500366":"NCID","subitem_1522646572813":"AA10779580"}]},"item_1617186941041":{"attribute_name":"Source Title","attribute_value_mlt":[{"subitem_1522650068558":"en","subitem_1522650091861":"Ryukyu mathematical journal"}]},"item_1617187056579":{"attribute_name":"Bibliographic Information","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2011-12","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"17","bibliographicPageStart":"1","bibliographicVolumeNumber":"24"}]},"item_1617258105262":{"attribute_name":"Resource Type","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_1617265215918":{"attribute_name":"Version Type","attribute_value_mlt":[{"subitem_1522305645492":"NA","subitem_1600292170262":"http://purl.org/coar/version/c_be7fb7dd8ff6fe43"}]},"item_1617605131499":{"attribute_name":"File","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_access","filename":"Vol24p001.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2006999/files/Vol24p001.pdf"},"version_id":"35862c11-9476-4774-92cb-9ba6762c271e"}]},"item_title":"COMPUTER-AIDED VERIFICATION OF THE GAUSS-BONNET FORMULA FOR CLOSED SURFACES","item_type_id":"15","owner":"1","path":["1642837638076","1642838406414"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2012-03-01"},"publish_date":"2012-03-01","publish_status":"0","recid":"2006999","relation_version_is_last":true,"title":["COMPUTER-AIDED VERIFICATION OF THE GAUSS-BONNET FORMULA FOR CLOSED SURFACES"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2022-10-31T03:13:02.867558+00:00"}