Liouville theorems for harmonic metrics on gradient Ricci solitons

In this paper, we prove two Liouville theorems for harmonic metrics on complex flat line bundles on gradient steady Ricci solitons and gradient shrinking K\"{a}hler-Ricci solitons, which imply that they arise from fundamental group representations into $S^1$.

Gespeichert in:

Bibliographische Detailangaben
Hauptverfasser:	He, Chenghong, Wu, Di, Zhang, Xi
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Complex Variables Mathematics - Differential Geometry
Online-Zugang:	Volltext bestellen
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page
container_issue
container_start_page
container_title
container_volume
creator	He, Chenghong Wu, Di Zhang, Xi
description	In this paper, we prove two Liouville theorems for harmonic metrics on complex flat line bundles on gradient steady Ricci solitons and gradient shrinking K\"{a}hler-Ricci solitons, which imply that they arise from fundamental group representations into $S^1$.
doi_str_mv	10.48550/arxiv.2411.12012
format	Article
fullrecord	<record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2411_12012</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2411_12012</sourcerecordid><originalsourceid>FETCH-arxiv_primary_2411_120123</originalsourceid><addsrcrecordid>eNqFzT0KAjEQQOE0FqIewMq5gDHZH7BWFAsrsQ8hZt2BJCOTuOjtxcXe6jUPPiGWWslm27ZqY_mFg6waraWulK6mYndGeg4YgofSe2IfM3TE0FuOlNBB9IXRZaAEd7Y39KnABZ1DyBSwUMpzMelsyH7x60ysjofr_rQeNfNgjJbf5quaUa3_Hx-uczfb</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Liouville theorems for harmonic metrics on gradient Ricci solitons</title><source>arXiv.org</source><creator>He, Chenghong ; Wu, Di ; Zhang, Xi</creator><creatorcontrib>He, Chenghong ; Wu, Di ; Zhang, Xi</creatorcontrib><description>In this paper, we prove two Liouville theorems for harmonic metrics on complex flat line bundles on gradient steady Ricci solitons and gradient shrinking K\"{a}hler-Ricci solitons, which imply that they arise from fundamental group representations into $S^1$.</description><identifier>DOI: 10.48550/arxiv.2411.12012</identifier><language>eng</language><subject>Mathematics - Complex Variables ; Mathematics - Differential Geometry</subject><creationdate>2024-11</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,781,886</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2411.12012$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2411.12012$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>He, Chenghong</creatorcontrib><creatorcontrib>Wu, Di</creatorcontrib><creatorcontrib>Zhang, Xi</creatorcontrib><title>Liouville theorems for harmonic metrics on gradient Ricci solitons</title><description>In this paper, we prove two Liouville theorems for harmonic metrics on complex flat line bundles on gradient steady Ricci solitons and gradient shrinking K\"{a}hler-Ricci solitons, which imply that they arise from fundamental group representations into $S^1$.</description><subject>Mathematics - Complex Variables</subject><subject>Mathematics - Differential Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNqFzT0KAjEQQOE0FqIewMq5gDHZH7BWFAsrsQ8hZt2BJCOTuOjtxcXe6jUPPiGWWslm27ZqY_mFg6waraWulK6mYndGeg4YgofSe2IfM3TE0FuOlNBB9IXRZaAEd7Y39KnABZ1DyBSwUMpzMelsyH7x60ysjofr_rQeNfNgjJbf5quaUa3_Hx-uczfb</recordid><startdate>20241118</startdate><enddate>20241118</enddate><creator>He, Chenghong</creator><creator>Wu, Di</creator><creator>Zhang, Xi</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20241118</creationdate><title>Liouville theorems for harmonic metrics on gradient Ricci solitons</title><author>He, Chenghong ; Wu, Di ; Zhang, Xi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2411_120123</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Complex Variables</topic><topic>Mathematics - Differential Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>He, Chenghong</creatorcontrib><creatorcontrib>Wu, Di</creatorcontrib><creatorcontrib>Zhang, Xi</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>He, Chenghong</au><au>Wu, Di</au><au>Zhang, Xi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Liouville theorems for harmonic metrics on gradient Ricci solitons</atitle><date>2024-11-18</date><risdate>2024</risdate><abstract>In this paper, we prove two Liouville theorems for harmonic metrics on complex flat line bundles on gradient steady Ricci solitons and gradient shrinking K\"{a}hler-Ricci solitons, which imply that they arise from fundamental group representations into $S^1$.</abstract><doi>10.48550/arxiv.2411.12012</doi><oa>free_for_read</oa></addata></record>
fulltext	fulltext_linktorsrc
identifier	DOI: 10.48550/arxiv.2411.12012
ispartof
issn
language	eng
recordid	cdi_arxiv_primary_2411_12012
source	arXiv.org
subjects	Mathematics - Complex Variables Mathematics - Differential Geometry
title	Liouville theorems for harmonic metrics on gradient Ricci solitons
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-13T17%3A32%3A31IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Liouville%20theorems%20for%20harmonic%20metrics%20on%20gradient%20Ricci%20solitons&rft.au=He,%20Chenghong&rft.date=2024-11-18&rft_id=info:doi/10.48550/arxiv.2411.12012&rft_dat=%3Carxiv_GOX%3E2411_12012%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true