Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds
In this article we discuss how to construct canonical strong Carrollian geometries at time/space like infinity of projectively compact Ricci flat Einstein manifolds ( M , g ) and discuss the links between the underlying projective structure of the metric g . The obtained Carrollian geometries are d...
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| Veröffentlicht in: | Geometriae dedicata 2025-02, Vol.219 (1), Article 12 |
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| container_title | Geometriae dedicata |
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| creator | Borthwick, Jack Herfray, Yannick |
| description | In this article we discuss how to construct canonical
strong
Carrollian geometries at time/space like infinity of projectively compact Ricci flat Einstein manifolds (
M
,
g
) and discuss the links between the underlying projective structure of the metric
g
. The obtained Carrollian geometries are determined by the data of the projective compactification. The key idea to achieve this is to consider a new type of Cartan geometry based on a non-effective homogeneous model for projective geometry. We prove that this structure is a general feature of projectively compact Ricci flat Einstein manifolds. |
| doi_str_mv | 10.1007/s10711-024-00973-5 |
| format | Article |
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strong
Carrollian geometries at time/space like infinity of projectively compact Ricci flat Einstein manifolds (
M
,
g
) and discuss the links between the underlying projective structure of the metric
g
. The obtained Carrollian geometries are determined by the data of the projective compactification. The key idea to achieve this is to consider a new type of Cartan geometry based on a non-effective homogeneous model for projective geometry. We prove that this structure is a general feature of projectively compact Ricci flat Einstein manifolds.</description><identifier>ISSN: 0046-5755</identifier><identifier>EISSN: 1572-9168</identifier><identifier>DOI: 10.1007/s10711-024-00973-5</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Algebraic Geometry ; Convex and Discrete Geometry ; Differential Geometry ; General Relativity and Quantum Cosmology ; Hyperbolic Geometry ; Infinity ; Mathematical Physics ; Mathematics ; Mathematics and Statistics ; Original Paper ; Physics ; Projective Geometry ; Topology</subject><ispartof>Geometriae dedicata, 2025-02, Vol.219 (1), Article 12</ispartof><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2024 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><rights>Copyright Springer Nature B.V. 2025</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c234t-11ef88024a7447c8a1ff3b5e9051c32de41863dead4c281201507d0f440cc40b3</cites><orcidid>0000-0002-5646-4301 ; 0000-0002-7183-0752</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10711-024-00973-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10711-024-00973-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,776,780,881,27903,27904,41467,42536,51298</link.rule.ids><backlink>$$Uhttps://hal.science/hal-04605759$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Borthwick, Jack</creatorcontrib><creatorcontrib>Herfray, Yannick</creatorcontrib><title>Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds</title><title>Geometriae dedicata</title><addtitle>Geom Dedicata</addtitle><description>In this article we discuss how to construct canonical
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Carrollian geometries at time/space like infinity of projectively compact Ricci flat Einstein manifolds (
M
,
g
) and discuss the links between the underlying projective structure of the metric
g
. The obtained Carrollian geometries are determined by the data of the projective compactification. The key idea to achieve this is to consider a new type of Cartan geometry based on a non-effective homogeneous model for projective geometry. We prove that this structure is a general feature of projectively compact Ricci flat Einstein manifolds.</description><subject>Algebraic Geometry</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>General Relativity and Quantum Cosmology</subject><subject>Hyperbolic Geometry</subject><subject>Infinity</subject><subject>Mathematical Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Physics</subject><subject>Projective Geometry</subject><subject>Topology</subject><issn>0046-5755</issn><issn>1572-9168</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2025</creationdate><recordtype>article</recordtype><recordid>eNp9kUFrVDEUhYMoOLb9A10FXLmIvTcvmWSWZaitMKCIrkOal9SM7yVjkhbm3zfjk7pzdeHyncO95xByifARAdRVRVCIDLhgABs1MPmKrFAqzja41q_JCkCsmVRSviXvat3DiVJ8RdrXkvfetfjkqU0j3dpS8jRFm-iDz7Nv5Uhtoy3O_qoerPNsir88jSnEFNuR5kQPLw7Tkbo8d6rRb9G5SMPUtTcx1eZjorNNMeRprOfkTbBT9Rd_5xn58enm-_aO7b7cft5e75jjg2gM0Qet-09WCaGcthjCcC_9BiS6gY9eoF4Po7ejcFwjB5SgRghCgHMC7ocz8mHx_WkncyhxtuVoso3m7npnTrseCvRQNk_Y2fcL29_5_ehrM_v8WFI_zwwotOZageoUXyhXcq3FhxdbBHNqwixNmH61-dOEkV00LKLa4fTgyz_r_6ieAZ0CjAE</recordid><startdate>20250201</startdate><enddate>20250201</enddate><creator>Borthwick, Jack</creator><creator>Herfray, Yannick</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-5646-4301</orcidid><orcidid>https://orcid.org/0000-0002-7183-0752</orcidid></search><sort><creationdate>20250201</creationdate><title>Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds</title><author>Borthwick, Jack ; Herfray, Yannick</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c234t-11ef88024a7447c8a1ff3b5e9051c32de41863dead4c281201507d0f440cc40b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2025</creationdate><topic>Algebraic Geometry</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>General Relativity and Quantum Cosmology</topic><topic>Hyperbolic Geometry</topic><topic>Infinity</topic><topic>Mathematical Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Physics</topic><topic>Projective Geometry</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Borthwick, Jack</creatorcontrib><creatorcontrib>Herfray, Yannick</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Geometriae dedicata</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Borthwick, Jack</au><au>Herfray, Yannick</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds</atitle><jtitle>Geometriae dedicata</jtitle><stitle>Geom Dedicata</stitle><date>2025-02-01</date><risdate>2025</risdate><volume>219</volume><issue>1</issue><artnum>12</artnum><issn>0046-5755</issn><eissn>1572-9168</eissn><abstract>In this article we discuss how to construct canonical
strong
Carrollian geometries at time/space like infinity of projectively compact Ricci flat Einstein manifolds (
M
,
g
) and discuss the links between the underlying projective structure of the metric
g
. The obtained Carrollian geometries are determined by the data of the projective compactification. The key idea to achieve this is to consider a new type of Cartan geometry based on a non-effective homogeneous model for projective geometry. We prove that this structure is a general feature of projectively compact Ricci flat Einstein manifolds.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10711-024-00973-5</doi><orcidid>https://orcid.org/0000-0002-5646-4301</orcidid><orcidid>https://orcid.org/0000-0002-7183-0752</orcidid></addata></record> |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Algebraic Geometry Convex and Discrete Geometry Differential Geometry General Relativity and Quantum Cosmology Hyperbolic Geometry Infinity Mathematical Physics Mathematics Mathematics and Statistics Original Paper Physics Projective Geometry Topology |
| title | Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds |
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