{"id":"https://openalex.org/W2989700503","doi":"https://doi.org/10.48550/arxiv.1911.10779","title":"Canonical coordinates on minimal time-like surfaces in the n-dimensional Minkowski space","display_name":"Canonical coordinates on minimal time-like surfaces in the n-dimensional Minkowski space","publication_year":2019,"publication_date":"2019-11-25","ids":{"openalex":"https://openalex.org/W2989700503","doi":"https://doi.org/10.48550/arxiv.1911.10779","mag":"2989700503"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1911.10779","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.10779","pdf_url":"https://arxiv.org/pdf/1911.10779","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1911.10779","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057406355","display_name":"Georgi Ganchev","orcid":"https://orcid.org/0000-0001-6941-6141","observed_orcids":["https://orcid.org/0000-0001-6941-6141"]},"institutions":[{"id":"https://openalex.org/I24768866","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03","country_code":"BG","type":"government","lineage":["https://openalex.org/I24768866"]},{"id":"https://openalex.org/I4210120207","display_name":"Todor Kableshkov University of Transport","ror":"https://ror.org/02myn8n47","country_code":"BG","type":"education","lineage":["https://openalex.org/I4210120207"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Ganchev, Georgi","raw_affiliation_strings":["Bulgarian Academy of Sciences , Institute of Mathematics and Informatics , Acad. G. Bonchev Str. bl. 8 , 1113 Sofia , Bulgaria","Department of Mathematics and Informatics , Todor Kableshkov University of Trans- port , 158 Geo Milev Str. , 1574 Sofia , Bulgaria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bulgarian Academy of Sciences , Institute of Mathematics and Informatics , Acad. G. Bonchev Str. bl. 8 , 1113 Sofia , Bulgaria","institution_ids":["https://openalex.org/I24768866"]},{"raw_affiliation_string":"Department of Mathematics and Informatics , Todor Kableshkov University of Trans- port , 158 Geo Milev Str. , 1574 Sofia , Bulgaria","institution_ids":["https://openalex.org/I4210120207"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046731565","display_name":"Krasimir Kanchev","orcid":"https://orcid.org/0000-0002-4460-3781","observed_orcids":["https://orcid.org/0000-0002-4460-3781"]},"institutions":[{"id":"https://openalex.org/I24768866","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03","country_code":"BG","type":"government","lineage":["https://openalex.org/I24768866"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Kanchev, Krasimir","raw_affiliation_strings":["Bulgarian Academy of Sciences , Institute of Mathematics and Informatics , Acad. G. Bonchev Str. bl. 8 , 1113 Sofia , Bulgaria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bulgarian Academy of Sciences , Institute of Mathematics and Informatics , Acad. G. Bonchev Str. bl. 8 , 1113 Sofia , Bulgaria","institution_ids":["https://openalex.org/I24768866"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9824000000953674,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9824000000953674,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.012199999764561653,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/canonical-coordinates","display_name":"canonical coordinates","score":0.8809999823570251},{"id":"https://openalex.org/keywords/first-fundamental-form","display_name":"first fundamental form","score":0.781000018119812},{"id":"https://openalex.org/keywords/complex-functions","display_name":"complex functions","score":0.4869999885559082},{"id":"https://openalex.org/keywords/normal-curvature","display_name":"normal curvature","score":0.8180000185966492},{"id":"https://openalex.org/keywords/surface-invariants","display_name":"surface invariants","score":0.6209999918937683}],"concepts":[{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.7934157848358154},{"id":"https://openalex.org/C145050668","wikidata":"https://www.wikidata.org/wiki/Q165301","display_name":"Hyperbola","level":2,"score":0.7557887434959412},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7549407482147217},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.6634979844093323},{"id":"https://openalex.org/C3379466","wikidata":"https://www.wikidata.org/wiki/Q1501876","display_name":"Canonical coordinates","level":3,"score":0.5359087586402893},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4870324730873108},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45793890953063965},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45424872636795044},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4356081783771515},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29271966218948364},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.125263512134552},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:1911.10779","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.10779","pdf_url":"https://arxiv.org/pdf/1911.10779","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2989700503","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1911.10779","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1911.10779","doi":"https://doi.org/10.48550/arxiv.1911.10779","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1911.10779","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1911.10779","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.10779","pdf_url":"https://arxiv.org/pdf/1911.10779","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1502045553","https://openalex.org/W2087284010","https://openalex.org/W2096506775","https://openalex.org/W2128000394","https://openalex.org/W2135288397","https://openalex.org/W2142082867","https://openalex.org/W2177630407","https://openalex.org/W2515925529","https://openalex.org/W2564852815","https://openalex.org/W2583666141","https://openalex.org/W2614272347","https://openalex.org/W2615759345","https://openalex.org/W3191639770"],"related_works":["https://openalex.org/W3104664976","https://openalex.org/W2991596336","https://openalex.org/W1676649682","https://openalex.org/W2564852815","https://openalex.org/W4390583901","https://openalex.org/W2069662328","https://openalex.org/W4392916275","https://openalex.org/W7132315071","https://openalex.org/W2747102145","https://openalex.org/W2615759345"],"abstract_inverted_index":{"We":[0,97],"introduce":[1,48],"canonical":[2,81,117],"coordinates":[3,27,82,118],"on":[4,83],"minimal":[5,84,107],"time-like":[6,45,85,108],"surfaces":[7,86],"in":[8,119],"the":[9,15,18,28,31,38,41,54,57,62,65,68,80,99,102,116,122],"n-dimensional":[10],"Minkowski":[11],"space":[12],"and":[13,17,60,110],"prove":[14],"existence":[16],"uniqueness":[19],"of":[20,30,40,56,67,101,105,115,121,124],"these":[21,26,77],"parameters.":[22],"With":[23],"respect":[24],"to":[25,75],"coefficients":[29],"first":[32],"fundamental":[33],"form":[34],"are":[35,87],"expressed":[36],"by":[37,89],"invariants":[39],"surface.":[42],"On":[43],"any":[44,106],"surface":[46,109],"we":[47],"a":[49,72,90,112],"special":[50],"complex":[51,95],"function":[52],"over":[53,64],"algebra":[55,66],"double":[58,69],"numbers":[59,70],"apply":[61],"analysis":[63],"as":[71],"convenient":[73],"tool":[74],"study":[76],"surfaces.":[78],"Then":[79],"characterized":[88],"natural":[91],"condition":[92],"for":[93],"this":[94,125],"function.":[96],"consider":[98],"hyperbola":[100],"normal":[103],"curvature":[104],"give":[111],"geometric":[113],"interpretation":[114],"terms":[120],"elements":[123],"hyperbola.":[126]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-09-30T09:27:27.532063","created_date":"2019-12-05T00:00:00"}
