The affine quasi-Einstein Equation for homogeneous surfaces

We study the affine quasi-Einstein Equation for homogeneous surfaces. This gives rise through the modified Riemannian extension to new half conformally flat generalized quasi-Einstein neutral signature (2, 2) manifolds, to conformally Einstein manifolds and also to new Einstein manifolds through a w...

Full description

Saved in:

Bibliographic Details
Published in:	Manuscripta mathematica Vol. 157; no. 1-2; pp. 279 - 294
Main Authors:	Brozos-Vázquez, M., García-Río, E., Gilkey, P., Valle-Regueiro, X.
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01-09-2018 Springer Nature B.V
Subjects:	Algebraic Geometry Calculus of Variations and Optimal Control; Optimization Einstein equations Geometry Lie Groups Manifolds Mathematics Mathematics and Statistics Number Theory Topological Groups 53B30 53C24 53C44 53C21
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	We study the affine quasi-Einstein Equation for homogeneous surfaces. This gives rise through the modified Riemannian extension to new half conformally flat generalized quasi-Einstein neutral signature (2, 2) manifolds, to conformally Einstein manifolds and also to new Einstein manifolds through a warped product construction.
AbstractList	We study the affine quasi-Einstein Equation for homogeneous surfaces. This gives rise through the modified Riemannian extension to new half conformally flat generalized quasi-Einstein neutral signature (2, 2) manifolds, to conformally Einstein manifolds and also to new Einstein manifolds through a warped product construction. We study the affine quasi-Einstein Equation for homogeneous surfaces. This gives rise through the modified Riemannian extension to new half conformally flat generalized quasi-Einstein neutral signature (2, 2) manifolds, to conformally Einstein manifolds and also to new Einstein manifolds through a warped product construction.
Author	García-Río, E. Valle-Regueiro, X. Brozos-Vázquez, M. Gilkey, P.
Author_xml	– sequence: 1 givenname: M. surname: Brozos-Vázquez fullname: Brozos-Vázquez, M. organization: Differential Geometry and its Applications Research Group, Escola Politécnica Superior, Universidade da Coruña – sequence: 2 givenname: E. orcidid: 0000-0003-1195-1664 surname: García-Río fullname: García-Río, E. email: eduardo.garcia.rio@usc.es organization: Faculty of Mathematics, University of Santiago de Compostela – sequence: 3 givenname: P. surname: Gilkey fullname: Gilkey, P. organization: Mathematics Department, University of Oregon – sequence: 4 givenname: X. surname: Valle-Regueiro fullname: Valle-Regueiro, X. organization: Faculty of Mathematics, University of Santiago de Compostela
BookMark	eNp1kMtKAzEUhoNUsFYfwN2A6-g5yUwygysp9QIFN3UdMpmknWKTNplZ-PamjODK1eHnvxz4rsnMB28JuUN4QAD5mAAYayigpNDUksoLMseSM4qyrmZknu2KMoF4Ra5T2gNkU_I5edrsbKGd670tTqNOPV31Pg2298Uq66EPvnAhFrtwCFvrbRhTkcbotLHphlw6_ZXs7e9dkM-X1Wb5Rtcfr-_L5zU1HMVAW1Pz0nWMV4J3oCVAJTtgXclrgxo6wZFptNqgqBkK3RgjmqplbVcyKXTLF-R-2j3GcBptGtQ-jNHnl4pBg0zIqqlzCqeUiSGlaJ06xv6g47dCUGdGamKkMiN1ZqRk7rCpk3LWb238W_6_9AOcdGoi
CitedBy_id	crossref_primary_10_1515_advgeom_2020_0011 crossref_primary_10_2200_S00917ED1V04Y201904MAS026
Cites_doi	10.1093/qmath/5.1.312 10.1090/S0002-9939-03-06878-3 10.1063/1.2209167 10.1016/j.difgeo.2004.03.005 10.1007/BF03322280 10.1098/rspa.2009.0046 10.1093/qmath/3.1.19 10.4171/051-1/8 10.2969/jmsj/07017479 10.1090/coll/008
ContentType	Journal Article
Copyright	Springer-Verlag GmbH Germany 2017 Copyright Springer Science & Business Media 2018
Copyright_xml	– notice: Springer-Verlag GmbH Germany 2017 – notice: Copyright Springer Science & Business Media 2018
DBID	AAYXX CITATION
DOI	10.1007/s00229-017-0987-7
DatabaseName	CrossRef
DatabaseTitle	CrossRef
DatabaseTitleList
DeliveryMethod	fulltext_linktorsrc
Discipline	Mathematics
EISSN	1432-1785
EndPage	294
ExternalDocumentID	10_1007_s00229_017_0987_7
GroupedDBID	--Z -52 -5D -5G -BR -EM -Y2 -~C -~X .86 .VR 06D 0R~ 0VY 199 1GH 1N0 1SB 2.D 203 29M 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2WC 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 692 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AABYN AAFGU AAHNG AAIAL AAJKR AANZL AAPBV AARHV AARTL AATNV AATVU AAUYE AAWCG AAYFA AAYIU AAYQN AAYTO ABBBX ABBXA ABDZT ABECU ABFGW ABFTV ABHLI ABHQN ABJNI ABJOX ABKAS ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACBMV ACBRV ACBXY ACBYP ACGFS ACHSB ACHXU ACIGE ACIPQ ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACTTH ACVWB ACWMK ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADMDM ADOXG ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEEQQ AEFIE AEFTE AEGAL AEGNC AEJHL AEJRE AEKMD AENEX AEOHA AEPOP AEPYU AESKC AESTI AETLH AEVLU AEVTX AEXYK AFDYV AFEXP AFGCZ AFLOW AFMKY AFNRJ AFQWF AFWTZ AFZKB AGAYW AGDGC AGGBP AGGDS AGJBK AGMZJ AGPAZ AGQMX AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIIXL AILAN AIMYW AITGF AJBLW AJDOV AJRNO AJZVZ AKQUC ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BBWZM BDATZ BGNMA CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAS LLZTM M4Y MA- MVM N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OK1 P19 P2P P9R PF- PT4 PT5 QOK QOS R4E R89 R9I REI RHV RIG RNI ROL RPX RSV RYB RZK RZZ S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TN5 TSG TSK TSV TUC TWZ U2A UG4 UNUBA UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 Y6R YLTOR YQT Z45 Z7U ZMTXR ZWQNP ~EX AACDK AAEOY AAJBT AASML AAYXX AAYZH ABAKF ACAOD ACDTI ACZOJ AEARS AEFQL AEMSY AFBBN AGQEE AGRTI AIGIU CITATION H13
ID	FETCH-LOGICAL-c316t-bc834fd23563d0a70057d02d438c1a0d6312a1eac168216a9cc695b2bd4276ab3
IEDL.DBID	AEJHL
ISSN	0025-2611
IngestDate	Tue Nov 05 22:19:14 EST 2024 Thu Nov 21 22:37:34 EST 2024 Sat Dec 16 12:02:54 EST 2023
IsPeerReviewed	true
IsScholarly	true
Issue	1-2
Keywords	53B30 53C24 53C44 53C21
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c316t-bc834fd23563d0a70057d02d438c1a0d6312a1eac168216a9cc695b2bd4276ab3
ORCID	0000-0003-1195-1664
PQID	2091267598
PQPubID	2043619
PageCount	16
ParticipantIDs	proquest_journals_2091267598 crossref_primary_10_1007_s00229_017_0987_7 springer_journals_10_1007_s00229_017_0987_7
PublicationCentury	2000
PublicationDate	2018-09-01
PublicationDateYYYYMMDD	2018-09-01
PublicationDate_xml	– month: 09 year: 2018 text: 2018-09-01 day: 01
PublicationDecade	2010
PublicationPlace	Berlin/Heidelberg
PublicationPlace_xml	– name: Berlin/Heidelberg – name: Heidelberg
PublicationTitle	Manuscripta mathematica
PublicationTitleAbbrev	manuscripta math
PublicationYear	2018
Publisher	Springer Berlin Heidelberg Springer Nature B.V
Publisher_xml	– name: Springer Berlin Heidelberg – name: Springer Nature B.V
References	CR2 Patterson, Walker (CR12) 1952; 3 CR4 CR3 CR7 CR9 Calviño-Louzao, García-Río, Gilkey, Vázquez-Lorenzo (CR5) 2009; 465 Steglich (CR13) 1995; 27 Nomizu, Sasaki (CR10) 1994 Opozda (CR11) 2004; 21 Derdzinski, Roter (CR6) 2006; 47 Kim, Kim (CR8) 2003; 131 Afifi (CR1) 1954; 5 Ch Steglich (987_CR13) 1995; 27 987_CR7 987_CR9 E Calviño-Louzao (987_CR5) 2009; 465 EM Patterson (987_CR12) 1952; 3 D-S Kim (987_CR8) 2003; 131 Z Afifi (987_CR1) 1954; 5 A Derdzinski (987_CR6) 2006; 47 987_CR3 987_CR2 K Nomizu (987_CR10) 1994 987_CR4 B Opozda (987_CR11) 2004; 21
References_xml	– volume: 5 start-page: 312 year: 1954 end-page: 320 ident: CR1 article-title: Riemann extensions of affine connected spaces publication-title: Q. J. Math. Oxf. Ser. (2) doi: 10.1093/qmath/5.1.312 contributor: fullname: Afifi – year: 1994 ident: CR10 publication-title: Affine Differential Geometry. Cambridge Tracts in Mathematics contributor: fullname: Sasaki – ident: CR3 – ident: CR4 – ident: CR2 – volume: 131 start-page: 2573 year: 2003 end-page: 2576 ident: CR8 article-title: Compact Einstein warped product spaces with nonpositive scalar curvature publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-03-06878-3 contributor: fullname: Kim – volume: 47 start-page: 062504 8 issue: 6 year: 2006 ident: CR6 article-title: Walker’s theorem without coordinates publication-title: J. Math. Phys. doi: 10.1063/1.2209167 contributor: fullname: Roter – ident: CR9 – volume: 21 start-page: 173 year: 2004 end-page: 198 ident: CR11 article-title: A classification of locally homogeneous connections on 2-dimensional manifolds publication-title: Differ. Geom. Appl. doi: 10.1016/j.difgeo.2004.03.005 contributor: fullname: Opozda – volume: 27 start-page: 188 year: 1995 end-page: 193 ident: CR13 article-title: Invariants of conformal and projective structures publication-title: Results Math. doi: 10.1007/BF03322280 contributor: fullname: Steglich – volume: 465 start-page: 2023 year: 2009 end-page: 2040 ident: CR5 article-title: The geometry of modified Riemannian extensions publication-title: Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. doi: 10.1098/rspa.2009.0046 contributor: fullname: Vázquez-Lorenzo – ident: CR7 – volume: 3 start-page: 19 year: 1952 end-page: 28 ident: CR12 article-title: Riemann extensions publication-title: Q. J. Math. Oxf. Ser. (2) doi: 10.1093/qmath/3.1.19 contributor: fullname: Walker – ident: 987_CR3 – volume: 465 start-page: 2023 year: 2009 ident: 987_CR5 publication-title: Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. doi: 10.1098/rspa.2009.0046 contributor: fullname: E Calviño-Louzao – volume: 27 start-page: 188 year: 1995 ident: 987_CR13 publication-title: Results Math. doi: 10.1007/BF03322280 contributor: fullname: Ch Steglich – volume-title: Affine Differential Geometry. Cambridge Tracts in Mathematics year: 1994 ident: 987_CR10 contributor: fullname: K Nomizu – ident: 987_CR9 doi: 10.4171/051-1/8 – volume: 3 start-page: 19 year: 1952 ident: 987_CR12 publication-title: Q. J. Math. Oxf. Ser. (2) doi: 10.1093/qmath/3.1.19 contributor: fullname: EM Patterson – ident: 987_CR4 – volume: 5 start-page: 312 year: 1954 ident: 987_CR1 publication-title: Q. J. Math. Oxf. Ser. (2) doi: 10.1093/qmath/5.1.312 contributor: fullname: Z Afifi – volume: 131 start-page: 2573 year: 2003 ident: 987_CR8 publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-03-06878-3 contributor: fullname: D-S Kim – ident: 987_CR2 doi: 10.2969/jmsj/07017479 – volume: 21 start-page: 173 year: 2004 ident: 987_CR11 publication-title: Differ. Geom. Appl. doi: 10.1016/j.difgeo.2004.03.005 contributor: fullname: B Opozda – ident: 987_CR7 doi: 10.1090/coll/008 – volume: 47 start-page: 062504 8 issue: 6 year: 2006 ident: 987_CR6 publication-title: J. Math. Phys. doi: 10.1063/1.2209167 contributor: fullname: A Derdzinski
SSID	ssj0014373
Score	2.197873
Snippet	We study the affine quasi-Einstein Equation for homogeneous surfaces. This gives rise through the modified Riemannian extension to new half conformally flat...
SourceID	proquest crossref springer
SourceType	Aggregation Database Publisher
StartPage	279
SubjectTerms	Algebraic Geometry Calculus of Variations and Optimal Control; Optimization Einstein equations Geometry Lie Groups Manifolds Mathematics Mathematics and Statistics Number Theory Topological Groups
Title	The affine quasi-Einstein Equation for homogeneous surfaces
URI	https://link.springer.com/article/10.1007/s00229-017-0987-7 https://www.proquest.com/docview/2091267598
Volume	157
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
link	http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PS8MwFA5uu-jB3-J0Sg-elEiTtEmKp6kdU3QIKngraZPiEFu3rv-_L1vboehBTz20hPL48r7v5SVfEDqRrqKKBQQbP2bYk57CcZyk2OWWbwJKEmUX3IaPYvQir0Nrk0ObpYvs7bzuSM4TdXPWzbKN3dojsAt1MhYt1AHq8QHbnX54O7xregfWrKe-qBXqA1L3Mn8a5CsbLSXmt67onGwGG__5zU20XklLp7_AwhZaMdk2WrtvfFmLHXQBqHBUmoK0dCalKsY4HIM-NOPMCScL028HVKzzmr_ngCyTl4VTlNPU7tvaRc-D8OlqiKvrE3DCCJ_hOJHMSzVlPmfaVcKeO9Uu1R6TCVGu5oxQRSDxEi4p4SpIEh74MY21RwVXMdtD7SzPzD5yICkYYUQaaA1sBpomFTw1RhqRxDxQQRed1mGMPhYuGVHjhzyPSAQRiWxEItFFvTrQUTVhighwQSgUL4HsorM6ssvXvw528KevD9EqCB652CPWQ-3ZtDRHqFXo8rhCETwHN6PLh08rVsEn
link.rule.ids	315,782,786,27933,27934,41073,42142,48344,48347,48357,49649,49652,49662,52153
linkProvider	Springer Nature
linkToHtml	http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PT8IwFH5ROKgHfxtR1B08aZqs7Wi7eCICwQhcxAROS9d2kYObMPb_2wKDaPSg5zVN8-Xtve_1vfcV4Fb4kkgaYmQaMUWBCCSKY5Ugn7l4ExKspLtw677wwUi02k4mh5azMItu97IkufDU62E3F25cbw9Hvk2UEd-GqhM7JxWoNkfjcWtdPHBqPeVLrTZBwGUx86dNvoajDcf8VhZdRJvOwb_OeQj7K3LpNZfWcARbJj2Gvf5amTU_gQdrF55MEksuvWkh8wlqTyxDNJPUa0-Xst-e5bHeW_aeWdsyWZF7eTFLXOfWKbx22sPHLlo9oIAUxWyOYiVokGhCG4xqX3I3eap9ogMqFJa-ZhQTia3rxUwQzGSoFAsbMYl1QDiTMT2DSpql5hw86xYMNzwJtbbxzLKahLPEGGG4ilkowxrclThGH0udjGitiLxAJLKIRA6RiNegXiIdrX6ZPLKWgYlNX0JRg_sS2c3nXze7-NPqG9jpDvu9qPc0eL6EXUt_xLJjrA6V-awwV7Cd6-J6ZVKfC_LDxw
linkToPdf	http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEB58gOjBt7g-e_CkBJukm6R4ENEu6xNBBW8lbRLcg93Vbv-_k-12RdGDeG4J4eNr5pvOzBeAAxVqpnlMiW1nnEQq0iTLckdC4eNNzGiu_Q-37oO8e1YXibfJOW1mYUbd7k1Jsp5p8C5NxfB4YNzxZPDNhx7f5yNJiEkzkdMwG2Eig0SfPUuuujeTQoJ37mlubcVkgTaFzZ8W-RqaPvXmtxLpKPJ0lv6952VYHIvO4KxmyQpM2WIVFm4njq3lGpwgXwLtHIrO4K3SZY8kPVSOtlcEyVttBx6gvg1e-q995JztV2VQVu_Od3Stw1MneTzvkvHFCiTnVAxJliseOcN4W3ATauknUk3ITMRVTnVoBKdMUzySqVCMCh3nuYjbGctMxKTQGd-AmaJf2E0I8Liw0koXG4NxDtWOk8JZq6zMMxHruAWHDabpoPbPSCdOySNEUkQk9YiksgU7Derp-FMqU2QMZZjWxKoFRw3Kn49_XWzrT2_vw9z9RSe9uby73oZ5VEWqbiTbgZnhe2V3Ybo01d6YXR8DKcxI
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The+affine+quasi-Einstein+Equation+for+homogeneous+surfaces&rft.jtitle=Manuscripta+mathematica&rft.au=Brozos-V%C3%A1zquez%2C+M.&rft.au=Garc%C3%ADa-R%C3%ADo%2C+E.&rft.au=Gilkey%2C+P.&rft.au=Valle-Regueiro%2C+X.&rft.date=2018-09-01&rft.pub=Springer+Berlin+Heidelberg&rft.issn=0025-2611&rft.eissn=1432-1785&rft.volume=157&rft.issue=1-2&rft.spage=279&rft.epage=294&rft_id=info:doi/10.1007%2Fs00229-017-0987-7&rft.externalDocID=10_1007_s00229_017_0987_7
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0025-2611&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0025-2611&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0025-2611&client=summon