On Almost Complex Structures on Six-dimensional Products of Spheres
In this paper, we discuss almost complex structures on the sphere S 6 and on the products of spheres S 3 × S 3 , S 1 × S 5 , and S 2 × S 4 . We prove that all almost complex Cayley structures that naturally appear from their embeddings into the Cayley octave algebra Ca are nonintegrable. We obtain e...
Gespeichert in:
| Veröffentlicht in: | Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-03, Vol.245 (5), p.568-600 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 600 |
|---|---|
| container_issue | 5 |
| container_start_page | 568 |
| container_title | Journal of mathematical sciences (New York, N.Y.) |
| container_volume | 245 |
| creator | Daurtseva, N. A. Smolentsev, N. K. |
| description | In this paper, we discuss almost complex structures on the sphere
S
6
and on the products of spheres
S
3
×
S
3
,
S
1
×
S
5
, and
S
2
×
S
4
. We prove that all almost complex Cayley structures that naturally appear from their embeddings into the Cayley octave algebra Ca are nonintegrable. We obtain expressions for the Nijenhuis tensor and the fundamental form ω for each gauge of the space Ca and prove the nondegeneracy of the form
d
ω. We show that through each point of a fiber of the twistor bundle over
S
6
, a one-parameter family of Cayley structures passes. We describe the set of
U
(2) ×
U
(2)- invariant Hermitian metrics on
S
3
×
S
3
and find estimates of the sectional sectional curvature. We consider the space of left-invariant, almost complex structures on
S
3
×
S
3
=
SU
(2) ×
SU
(2) and prove the properties of left-invariant structures that yield the maximal value of the norm of the Nijenhuis tensor on the set of left-invariant, orthogonal, almost complex structures. |
| doi_str_mv | 10.1007/s10958-020-04712-5 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_proqu</sourceid><recordid>TN_cdi_proquest_journals_2354776259</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A618761470</galeid><sourcerecordid>A618761470</sourcerecordid><originalsourceid>FETCH-LOGICAL-c3735-c730ae3d8b98131b50e229fc299c45045843f0d9035bfdfed9ca5ff711e694553</originalsourceid><addsrcrecordid>eNp9kV1LwzAUhosoOKd_wKuCV15k5qNpmssx_BgMJk6vQ5aezI62mUkL89-bOWEMhuQiIed5DofzJsktwSOCsXgIBEteIEwxwpkgFPGzZEC4YKgQkp_HNxYUMSayy-QqhDWOUl6wQTKZt-m4blzo0olrNjVs00Xne9P1HkLq2nRRbVFZNdCGyrW6Tl-9K2M51my62HxCxK6TC6vrADd_9zD5eHp8n7yg2fx5OhnPkGGCcWQEwxpYWSxlQRhZcgyUSmuolCbjOONFxiwuJWZ8aUsLpTSaWysIgVxmnLNhcrfvu_Huq4fQqbXrfRwqKMp4JkROuTxQK12DqlrrOq9NUwWjxjkpRE4ygSOFTlAraMHr2rVgq_h9xI9O8PGU0FTmpHB_JESmg2230n0Iarp4O2bpnjXeheDBqo2vGu2_FcFql6_a56tivuo3X7XbBttLIcLtCvxhG_9YP8ofpC8</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2354776259</pqid></control><display><type>article</type><title>On Almost Complex Structures on Six-dimensional Products of Spheres</title><source>Springer Nature - Complete Springer Journals</source><creator>Daurtseva, N. A. ; Smolentsev, N. K.</creator><creatorcontrib>Daurtseva, N. A. ; Smolentsev, N. K.</creatorcontrib><description>In this paper, we discuss almost complex structures on the sphere
S
6
and on the products of spheres
S
3
×
S
3
,
S
1
×
S
5
, and
S
2
×
S
4
. We prove that all almost complex Cayley structures that naturally appear from their embeddings into the Cayley octave algebra Ca are nonintegrable. We obtain expressions for the Nijenhuis tensor and the fundamental form ω for each gauge of the space Ca and prove the nondegeneracy of the form
d
ω. We show that through each point of a fiber of the twistor bundle over
S
6
, a one-parameter family of Cayley structures passes. We describe the set of
U
(2) ×
U
(2)- invariant Hermitian metrics on
S
3
×
S
3
and find estimates of the sectional sectional curvature. We consider the space of left-invariant, almost complex structures on
S
3
×
S
3
=
SU
(2) ×
SU
(2) and prove the properties of left-invariant structures that yield the maximal value of the norm of the Nijenhuis tensor on the set of left-invariant, orthogonal, almost complex structures.</description><identifier>ISSN: 1072-3374</identifier><identifier>EISSN: 1573-8795</identifier><identifier>DOI: 10.1007/s10958-020-04712-5</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Invariants ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Tensors</subject><ispartof>Journal of mathematical sciences (New York, N.Y.), 2020-03, Vol.245 (5), p.568-600</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020</rights><rights>COPYRIGHT 2020 Springer</rights><rights>2020© Springer Science+Business Media, LLC, part of Springer Nature 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3735-c730ae3d8b98131b50e229fc299c45045843f0d9035bfdfed9ca5ff711e694553</citedby><cites>FETCH-LOGICAL-c3735-c730ae3d8b98131b50e229fc299c45045843f0d9035bfdfed9ca5ff711e694553</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10958-020-04712-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10958-020-04712-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Daurtseva, N. A.</creatorcontrib><creatorcontrib>Smolentsev, N. K.</creatorcontrib><title>On Almost Complex Structures on Six-dimensional Products of Spheres</title><title>Journal of mathematical sciences (New York, N.Y.)</title><addtitle>J Math Sci</addtitle><description>In this paper, we discuss almost complex structures on the sphere
S
6
and on the products of spheres
S
3
×
S
3
,
S
1
×
S
5
, and
S
2
×
S
4
. We prove that all almost complex Cayley structures that naturally appear from their embeddings into the Cayley octave algebra Ca are nonintegrable. We obtain expressions for the Nijenhuis tensor and the fundamental form ω for each gauge of the space Ca and prove the nondegeneracy of the form
d
ω. We show that through each point of a fiber of the twistor bundle over
S
6
, a one-parameter family of Cayley structures passes. We describe the set of
U
(2) ×
U
(2)- invariant Hermitian metrics on
S
3
×
S
3
and find estimates of the sectional sectional curvature. We consider the space of left-invariant, almost complex structures on
S
3
×
S
3
=
SU
(2) ×
SU
(2) and prove the properties of left-invariant structures that yield the maximal value of the norm of the Nijenhuis tensor on the set of left-invariant, orthogonal, almost complex structures.</description><subject>Algebra</subject><subject>Invariants</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Tensors</subject><issn>1072-3374</issn><issn>1573-8795</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kV1LwzAUhosoOKd_wKuCV15k5qNpmssx_BgMJk6vQ5aezI62mUkL89-bOWEMhuQiIed5DofzJsktwSOCsXgIBEteIEwxwpkgFPGzZEC4YKgQkp_HNxYUMSayy-QqhDWOUl6wQTKZt-m4blzo0olrNjVs00Xne9P1HkLq2nRRbVFZNdCGyrW6Tl-9K2M51my62HxCxK6TC6vrADd_9zD5eHp8n7yg2fx5OhnPkGGCcWQEwxpYWSxlQRhZcgyUSmuolCbjOONFxiwuJWZ8aUsLpTSaWysIgVxmnLNhcrfvu_Huq4fQqbXrfRwqKMp4JkROuTxQK12DqlrrOq9NUwWjxjkpRE4ygSOFTlAraMHr2rVgq_h9xI9O8PGU0FTmpHB_JESmg2230n0Iarp4O2bpnjXeheDBqo2vGu2_FcFql6_a56tivuo3X7XbBttLIcLtCvxhG_9YP8ofpC8</recordid><startdate>20200304</startdate><enddate>20200304</enddate><creator>Daurtseva, N. A.</creator><creator>Smolentsev, N. K.</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ISR</scope></search><sort><creationdate>20200304</creationdate><title>On Almost Complex Structures on Six-dimensional Products of Spheres</title><author>Daurtseva, N. A. ; Smolentsev, N. K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3735-c730ae3d8b98131b50e229fc299c45045843f0d9035bfdfed9ca5ff711e694553</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Algebra</topic><topic>Invariants</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Tensors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Daurtseva, N. A.</creatorcontrib><creatorcontrib>Smolentsev, N. K.</creatorcontrib><collection>CrossRef</collection><collection>Gale In Context: Science</collection><jtitle>Journal of mathematical sciences (New York, N.Y.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Daurtseva, N. A.</au><au>Smolentsev, N. K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Almost Complex Structures on Six-dimensional Products of Spheres</atitle><jtitle>Journal of mathematical sciences (New York, N.Y.)</jtitle><stitle>J Math Sci</stitle><date>2020-03-04</date><risdate>2020</risdate><volume>245</volume><issue>5</issue><spage>568</spage><epage>600</epage><pages>568-600</pages><issn>1072-3374</issn><eissn>1573-8795</eissn><abstract>In this paper, we discuss almost complex structures on the sphere
S
6
and on the products of spheres
S
3
×
S
3
,
S
1
×
S
5
, and
S
2
×
S
4
. We prove that all almost complex Cayley structures that naturally appear from their embeddings into the Cayley octave algebra Ca are nonintegrable. We obtain expressions for the Nijenhuis tensor and the fundamental form ω for each gauge of the space Ca and prove the nondegeneracy of the form
d
ω. We show that through each point of a fiber of the twistor bundle over
S
6
, a one-parameter family of Cayley structures passes. We describe the set of
U
(2) ×
U
(2)- invariant Hermitian metrics on
S
3
×
S
3
and find estimates of the sectional sectional curvature. We consider the space of left-invariant, almost complex structures on
S
3
×
S
3
=
SU
(2) ×
SU
(2) and prove the properties of left-invariant structures that yield the maximal value of the norm of the Nijenhuis tensor on the set of left-invariant, orthogonal, almost complex structures.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10958-020-04712-5</doi><tpages>33</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1072-3374 |
| ispartof | Journal of mathematical sciences (New York, N.Y.), 2020-03, Vol.245 (5), p.568-600 |
| issn | 1072-3374 1573-8795 |
| language | eng |
| recordid | cdi_proquest_journals_2354776259 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Algebra Invariants Mathematical analysis Mathematics Mathematics and Statistics Tensors |
| title | On Almost Complex Structures on Six-dimensional Products of Spheres |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-21T10%3A57%3A22IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20Almost%20Complex%20Structures%20on%20Six-dimensional%20Products%20of%20Spheres&rft.jtitle=Journal%20of%20mathematical%20sciences%20(New%20York,%20N.Y.)&rft.au=Daurtseva,%20N.%20A.&rft.date=2020-03-04&rft.volume=245&rft.issue=5&rft.spage=568&rft.epage=600&rft.pages=568-600&rft.issn=1072-3374&rft.eissn=1573-8795&rft_id=info:doi/10.1007/s10958-020-04712-5&rft_dat=%3Cgale_proqu%3EA618761470%3C/gale_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2354776259&rft_id=info:pmid/&rft_galeid=A618761470&rfr_iscdi=true |