Specificity of Petrov Classification of (Anti-)Self-Dual Zero Signature Metrics
A.Z. Petrov divided 4-metrics of signature 0 into 6 types, which later began to be denoted by I , D , O , II , N , III . However, in the case of (anti-)self-duality, the -matrix, on the basis of which Petrov built his classification, acquires specificity. First, the determinant of this -matrix has a...
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| creator | Krivonosov, L. N. Luk’yanov, V. A. |
| description | A.Z. Petrov divided 4-metrics of signature 0 into 6 types, which later began to be denoted by
I
,
D
,
O
,
II
,
N
,
III
. However, in the case of (anti-)self-duality, the
-matrix, on the basis of which Petrov built his classification, acquires specificity. First, the determinant of this
-matrix has a root 0 of multiplicity at least 3. Second, the multiplicity of this root cannot be 5. These two circumstances lead to the fact that there are not 6, but 7 different types of metrics. A new type
I
appears, whose characteristic number 0 has multiplicity 4. This type does not coincide with
I
, since for type
I
the multiplicity of the root 0 is three. Examples of metrics, expressed in terms of elementary functions, of all 7 types are constructed. |
| doi_str_mv | 10.3103/S1066369X20090054 |
| format | Article |
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I
,
D
,
O
,
II
,
N
,
III
. However, in the case of (anti-)self-duality, the
-matrix, on the basis of which Petrov built his classification, acquires specificity. First, the determinant of this
-matrix has a root 0 of multiplicity at least 3. Second, the multiplicity of this root cannot be 5. These two circumstances lead to the fact that there are not 6, but 7 different types of metrics. A new type
I
appears, whose characteristic number 0 has multiplicity 4. This type does not coincide with
I
, since for type
I
the multiplicity of the root 0 is three. Examples of metrics, expressed in terms of elementary functions, of all 7 types are constructed.</description><identifier>ISSN: 1066-369X</identifier><identifier>EISSN: 1934-810X</identifier><identifier>DOI: 10.3103/S1066369X20090054</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Classification ; Mathematics ; Mathematics and Statistics</subject><ispartof>Russian mathematics, 2020-09, Vol.64 (9), p.50-60</ispartof><rights>Allerton Press, Inc. 2020</rights><rights>Allerton Press, Inc. 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-fa44ef48400eb08b9feb434ab68a73f15b6c7926e009a35a7e97c477385f11e43</citedby><cites>FETCH-LOGICAL-c316t-fa44ef48400eb08b9feb434ab68a73f15b6c7926e009a35a7e97c477385f11e43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.3103/S1066369X20090054$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.3103/S1066369X20090054$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Krivonosov, L. N.</creatorcontrib><creatorcontrib>Luk’yanov, V. A.</creatorcontrib><title>Specificity of Petrov Classification of (Anti-)Self-Dual Zero Signature Metrics</title><title>Russian mathematics</title><addtitle>Russ Math</addtitle><description>A.Z. Petrov divided 4-metrics of signature 0 into 6 types, which later began to be denoted by
I
,
D
,
O
,
II
,
N
,
III
. However, in the case of (anti-)self-duality, the
-matrix, on the basis of which Petrov built his classification, acquires specificity. First, the determinant of this
-matrix has a root 0 of multiplicity at least 3. Second, the multiplicity of this root cannot be 5. These two circumstances lead to the fact that there are not 6, but 7 different types of metrics. A new type
I
appears, whose characteristic number 0 has multiplicity 4. This type does not coincide with
I
, since for type
I
the multiplicity of the root 0 is three. Examples of metrics, expressed in terms of elementary functions, of all 7 types are constructed.</description><subject>Classification</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1066-369X</issn><issn>1934-810X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp1kE9LxDAQxYMouK5-AG8FL3qIJk2aNsdl_QsrK1Rh8VLSMFmy1GZNUmG_vSkreBBPM8z7vRnmIXROyTWjhN3UlAjBhFzlhEhCCn6AJlQyjitKVoepTzIe9WN0EsImESLnYoKW9Ra0NVbbuMucyV4geveVzTsVwjhW0bp-FC5nfbT4qobO4NtBddk7eJfVdt2rOHjInpPR6nCKjozqApz91Cl6u797nT_ixfLhaT5bYM2oiNgozsHwihMCLalaaaDljKtWVKpkhhat0KXMBaRvFCtUCbLUvCxZVRhKgbMputjv3Xr3OUCIzcYNvk8nm5wXlElZVCJRdE9p70LwYJqttx_K7xpKmjG35k9uyZPvPSGx_Rr87-b_Td_ReW5k</recordid><startdate>20200901</startdate><enddate>20200901</enddate><creator>Krivonosov, L. N.</creator><creator>Luk’yanov, V. A.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20200901</creationdate><title>Specificity of Petrov Classification of (Anti-)Self-Dual Zero Signature Metrics</title><author>Krivonosov, L. N. ; Luk’yanov, V. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-fa44ef48400eb08b9feb434ab68a73f15b6c7926e009a35a7e97c477385f11e43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Classification</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Krivonosov, L. N.</creatorcontrib><creatorcontrib>Luk’yanov, V. A.</creatorcontrib><collection>CrossRef</collection><jtitle>Russian mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Krivonosov, L. N.</au><au>Luk’yanov, V. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Specificity of Petrov Classification of (Anti-)Self-Dual Zero Signature Metrics</atitle><jtitle>Russian mathematics</jtitle><stitle>Russ Math</stitle><date>2020-09-01</date><risdate>2020</risdate><volume>64</volume><issue>9</issue><spage>50</spage><epage>60</epage><pages>50-60</pages><issn>1066-369X</issn><eissn>1934-810X</eissn><abstract>A.Z. Petrov divided 4-metrics of signature 0 into 6 types, which later began to be denoted by
I
,
D
,
O
,
II
,
N
,
III
. However, in the case of (anti-)self-duality, the
-matrix, on the basis of which Petrov built his classification, acquires specificity. First, the determinant of this
-matrix has a root 0 of multiplicity at least 3. Second, the multiplicity of this root cannot be 5. These two circumstances lead to the fact that there are not 6, but 7 different types of metrics. A new type
I
appears, whose characteristic number 0 has multiplicity 4. This type does not coincide with
I
, since for type
I
the multiplicity of the root 0 is three. Examples of metrics, expressed in terms of elementary functions, of all 7 types are constructed.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.3103/S1066369X20090054</doi><tpages>11</tpages></addata></record> |
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| language | eng |
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| subjects | Classification Mathematics Mathematics and Statistics |
| title | Specificity of Petrov Classification of (Anti-)Self-Dual Zero Signature Metrics |
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