On the ergodicity of the frame flow on even-dimensional manifolds
It is known that the frame flow on a closed n -dimensional Riemannian manifold with negative sectional curvature is ergodic if n is odd and n ≠ 7 . In this paper we study its ergodicity in the remaining cases. For n even and n ≠ 8 , 134 , we show that: if n ≡ 2 mod 4 or n = 4 , the frame flow is erg...
Gespeichert in:
| Veröffentlicht in: | Inventiones mathematicae 2024-12, Vol.238 (3), p.1067-1110 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1110 |
|---|---|
| container_issue | 3 |
| container_start_page | 1067 |
| container_title | Inventiones mathematicae |
| container_volume | 238 |
| creator | Cekić, Mihajlo Lefeuvre, Thibault Moroianu, Andrei Semmelmann, Uwe |
| description | It is known that the frame flow on a closed
n
-dimensional Riemannian manifold with negative sectional curvature is ergodic if
n
is odd and
n
≠
7
. In this paper we study its ergodicity in the remaining cases. For
n
even and
n
≠
8
,
134
, we show that:
if
n
≡
2
mod 4 or
n
=
4
, the frame flow is ergodic if the manifold is
∼
0.3
-pinched,
if
n
≡
0
mod 4, it is ergodic if the manifold is
∼
0.6
-pinched.
In the three dimensions
n
=
7
,
8
,
134
, the respective pinching bounds that we need in order to prove ergodicity are 0.4962..., 0.6212..., and 0.5788... This is a significant improvement over the previously known results and a step forward towards solving a long-standing conjecture of Brin asserting that 0.25-pinched even-dimensional manifolds have an ergodic frame flow. |
| doi_str_mv | 10.1007/s00222-024-01297-7 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3128018297</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3128018297</sourcerecordid><originalsourceid>FETCH-LOGICAL-c244t-d848200ad2e694aa431f0cfdf8f3d24fa89d20f232a3649de4a09b589b1a686d3</originalsourceid><addsrcrecordid>eNp9UE1LAzEQDaJgrf4BTwueo5NJ3E2OpagVCr3oOaSbpG7Z3dRkq_Tfm3YFb15mmHkfzDxCbhncM4DqIQEgIgUUFBiqilZnZMIER3qczskk40CVYnBJrlLaAmSwwgmZrfpi-HCFi5tgm7oZDkXwp42Ppsu1Dd9F6Av35Xpqm871qQm9aYvO9I0PrU3X5MKbNrmb3z4l789Pb_MFXa5eXuezJa1RiIFaKSQCGIuuVMIYwZmH2lsvPbcovJHKInjkaHgplHXCgFo_SrVmppSl5VNyN_ruYvjcuzTobdjHfErSnKEEJvOnmYUjq44hpei83sWmM_GgGehjVHqMSueo9CkqfRTxUZQyud-4-Gf9j-oH8aprGQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3128018297</pqid></control><display><type>article</type><title>On the ergodicity of the frame flow on even-dimensional manifolds</title><source>SpringerNature Journals</source><creator>Cekić, Mihajlo ; Lefeuvre, Thibault ; Moroianu, Andrei ; Semmelmann, Uwe</creator><creatorcontrib>Cekić, Mihajlo ; Lefeuvre, Thibault ; Moroianu, Andrei ; Semmelmann, Uwe</creatorcontrib><description>It is known that the frame flow on a closed
n
-dimensional Riemannian manifold with negative sectional curvature is ergodic if
n
is odd and
n
≠
7
. In this paper we study its ergodicity in the remaining cases. For
n
even and
n
≠
8
,
134
, we show that:
if
n
≡
2
mod 4 or
n
=
4
, the frame flow is ergodic if the manifold is
∼
0.3
-pinched,
if
n
≡
0
mod 4, it is ergodic if the manifold is
∼
0.6
-pinched.
In the three dimensions
n
=
7
,
8
,
134
, the respective pinching bounds that we need in order to prove ergodicity are 0.4962..., 0.6212..., and 0.5788... This is a significant improvement over the previously known results and a step forward towards solving a long-standing conjecture of Brin asserting that 0.25-pinched even-dimensional manifolds have an ergodic frame flow.</description><identifier>ISSN: 0020-9910</identifier><identifier>EISSN: 1432-1297</identifier><identifier>DOI: 10.1007/s00222-024-01297-7</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Ergodic processes ; Mathematics ; Mathematics and Statistics ; Riemann manifold</subject><ispartof>Inventiones mathematicae, 2024-12, Vol.238 (3), p.1067-1110</ispartof><rights>The Author(s) 2024</rights><rights>The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c244t-d848200ad2e694aa431f0cfdf8f3d24fa89d20f232a3649de4a09b589b1a686d3</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/s00222-024-01297-7$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00222-024-01297-7$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Cekić, Mihajlo</creatorcontrib><creatorcontrib>Lefeuvre, Thibault</creatorcontrib><creatorcontrib>Moroianu, Andrei</creatorcontrib><creatorcontrib>Semmelmann, Uwe</creatorcontrib><title>On the ergodicity of the frame flow on even-dimensional manifolds</title><title>Inventiones mathematicae</title><addtitle>Invent. math</addtitle><description>It is known that the frame flow on a closed
n
-dimensional Riemannian manifold with negative sectional curvature is ergodic if
n
is odd and
n
≠
7
. In this paper we study its ergodicity in the remaining cases. For
n
even and
n
≠
8
,
134
, we show that:
if
n
≡
2
mod 4 or
n
=
4
, the frame flow is ergodic if the manifold is
∼
0.3
-pinched,
if
n
≡
0
mod 4, it is ergodic if the manifold is
∼
0.6
-pinched.
In the three dimensions
n
=
7
,
8
,
134
, the respective pinching bounds that we need in order to prove ergodicity are 0.4962..., 0.6212..., and 0.5788... This is a significant improvement over the previously known results and a step forward towards solving a long-standing conjecture of Brin asserting that 0.25-pinched even-dimensional manifolds have an ergodic frame flow.</description><subject>Ergodic processes</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Riemann manifold</subject><issn>0020-9910</issn><issn>1432-1297</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9UE1LAzEQDaJgrf4BTwueo5NJ3E2OpagVCr3oOaSbpG7Z3dRkq_Tfm3YFb15mmHkfzDxCbhncM4DqIQEgIgUUFBiqilZnZMIER3qczskk40CVYnBJrlLaAmSwwgmZrfpi-HCFi5tgm7oZDkXwp42Ppsu1Dd9F6Av35Xpqm871qQm9aYvO9I0PrU3X5MKbNrmb3z4l789Pb_MFXa5eXuezJa1RiIFaKSQCGIuuVMIYwZmH2lsvPbcovJHKInjkaHgplHXCgFo_SrVmppSl5VNyN_ruYvjcuzTobdjHfErSnKEEJvOnmYUjq44hpei83sWmM_GgGehjVHqMSueo9CkqfRTxUZQyud-4-Gf9j-oH8aprGQ</recordid><startdate>20241201</startdate><enddate>20241201</enddate><creator>Cekić, Mihajlo</creator><creator>Lefeuvre, Thibault</creator><creator>Moroianu, Andrei</creator><creator>Semmelmann, Uwe</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20241201</creationdate><title>On the ergodicity of the frame flow on even-dimensional manifolds</title><author>Cekić, Mihajlo ; Lefeuvre, Thibault ; Moroianu, Andrei ; Semmelmann, Uwe</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c244t-d848200ad2e694aa431f0cfdf8f3d24fa89d20f232a3649de4a09b589b1a686d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Ergodic processes</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Riemann manifold</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cekić, Mihajlo</creatorcontrib><creatorcontrib>Lefeuvre, Thibault</creatorcontrib><creatorcontrib>Moroianu, Andrei</creatorcontrib><creatorcontrib>Semmelmann, Uwe</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Inventiones mathematicae</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cekić, Mihajlo</au><au>Lefeuvre, Thibault</au><au>Moroianu, Andrei</au><au>Semmelmann, Uwe</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the ergodicity of the frame flow on even-dimensional manifolds</atitle><jtitle>Inventiones mathematicae</jtitle><stitle>Invent. math</stitle><date>2024-12-01</date><risdate>2024</risdate><volume>238</volume><issue>3</issue><spage>1067</spage><epage>1110</epage><pages>1067-1110</pages><issn>0020-9910</issn><eissn>1432-1297</eissn><abstract>It is known that the frame flow on a closed
n
-dimensional Riemannian manifold with negative sectional curvature is ergodic if
n
is odd and
n
≠
7
. In this paper we study its ergodicity in the remaining cases. For
n
even and
n
≠
8
,
134
, we show that:
if
n
≡
2
mod 4 or
n
=
4
, the frame flow is ergodic if the manifold is
∼
0.3
-pinched,
if
n
≡
0
mod 4, it is ergodic if the manifold is
∼
0.6
-pinched.
In the three dimensions
n
=
7
,
8
,
134
, the respective pinching bounds that we need in order to prove ergodicity are 0.4962..., 0.6212..., and 0.5788... This is a significant improvement over the previously known results and a step forward towards solving a long-standing conjecture of Brin asserting that 0.25-pinched even-dimensional manifolds have an ergodic frame flow.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00222-024-01297-7</doi><tpages>44</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0020-9910 |
| ispartof | Inventiones mathematicae, 2024-12, Vol.238 (3), p.1067-1110 |
| issn | 0020-9910 1432-1297 |
| language | eng |
| recordid | cdi_proquest_journals_3128018297 |
| source | SpringerNature Journals |
| subjects | Ergodic processes Mathematics Mathematics and Statistics Riemann manifold |
| title | On the ergodicity of the frame flow on even-dimensional manifolds |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-24T21%3A58%3A34IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20ergodicity%20of%20the%20frame%20flow%20on%20even-dimensional%20manifolds&rft.jtitle=Inventiones%20mathematicae&rft.au=Ceki%C4%87,%20Mihajlo&rft.date=2024-12-01&rft.volume=238&rft.issue=3&rft.spage=1067&rft.epage=1110&rft.pages=1067-1110&rft.issn=0020-9910&rft.eissn=1432-1297&rft_id=info:doi/10.1007/s00222-024-01297-7&rft_dat=%3Cproquest_cross%3E3128018297%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3128018297&rft_id=info:pmid/&rfr_iscdi=true |