{"_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": ["1642837638076", "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": "\u795e\u5c71, \u9756\u5f66", "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^\u221e-surface with Euler-Poincar\u00e9 characteristic _X(X), has a Riemannian metric, and if K : X \u2192 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, (2\u03c0)/1 \u222b_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^\u221e-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": "\u7d00\u8981\u8ad6\u6587", "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": [{"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", "download_preview_message": "", "file_order": 0, "filename": "Vol24p001.pdf", "future_date_message": "", "is_thumbnail": false, "mimetype": "", "size": 0, "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"], "permalink_uri": "http://hdl.handle.net/20.500.12000/23589", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2012-03-01"}, "publish_date": "2012-03-01", "publish_status": "0", "recid": "2006999", "relation": {}, "relation_version_is_last": true, "title": ["COMPUTER-AIDED VERIFICATION OF THE GAUSS-BONNET FORMULA FOR CLOSED SURFACES"], "weko_shared_id": -1}