The evolution of positively curved invariant Riemannian metrics on the Wallach spaces under the Ricci flow
This paper is devoted to the study of the evolution of positively curved metrics on the Wallach spaces SU ( 3 ) / T max , Sp ( 3 ) / Sp ( 1 ) × Sp ( 1 ) × Sp ( 1 ) , and F 4 / Spin ( 8 ) . We prove that for all Wallach spaces, the normalized Ricci flow evolves all generic invariant Riemannian metric...
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| Veröffentlicht in: | Annals of global analysis and geometry 2016-07, Vol.50 (1), p.65-84 |
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| creator | Abiev, Nurlan Abievich Nikonorov, Yuriĭ Gennadievich |
| description | This paper is devoted to the study of the evolution of positively curved metrics on the Wallach spaces
SU
(
3
)
/
T
max
,
Sp
(
3
)
/
Sp
(
1
)
×
Sp
(
1
)
×
Sp
(
1
)
, and
F
4
/
Spin
(
8
)
. We prove that for all Wallach spaces, the normalized Ricci flow evolves all generic invariant Riemannian metrics with positive sectional curvature into metrics with mixed sectional curvature. Moreover, we prove that for the spaces
Sp
(
3
)
/
Sp
(
1
)
×
Sp
(
1
)
×
Sp
(
1
)
and
F
4
/
Spin
(
8
)
, the normalized Ricci flow evolves all generic invariant Riemannian metrics with positive Ricci curvature into metrics with mixed Ricci curvature. We also get similar results for some more general homogeneous spaces. |
| doi_str_mv | 10.1007/s10455-016-9502-8 |
| format | Article |
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SU
(
3
)
/
T
max
,
Sp
(
3
)
/
Sp
(
1
)
×
Sp
(
1
)
×
Sp
(
1
)
, and
F
4
/
Spin
(
8
)
. We prove that for all Wallach spaces, the normalized Ricci flow evolves all generic invariant Riemannian metrics with positive sectional curvature into metrics with mixed sectional curvature. Moreover, we prove that for the spaces
Sp
(
3
)
/
Sp
(
1
)
×
Sp
(
1
)
×
Sp
(
1
)
and
F
4
/
Spin
(
8
)
, the normalized Ricci flow evolves all generic invariant Riemannian metrics with positive Ricci curvature into metrics with mixed Ricci curvature. We also get similar results for some more general homogeneous spaces.</description><identifier>ISSN: 0232-704X</identifier><identifier>EISSN: 1572-9060</identifier><identifier>DOI: 10.1007/s10455-016-9502-8</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Algebra ; Analysis ; Curvature ; Curved ; Differential Geometry ; Evolution ; Geometry ; Global Analysis and Analysis on Manifolds ; Invariants ; Mathematical analysis ; Mathematical models ; Mathematical Physics ; Mathematics ; Mathematics and Statistics ; Studies ; Texts ; Theorems ; Topological manifolds</subject><ispartof>Annals of global analysis and geometry, 2016-07, Vol.50 (1), p.65-84</ispartof><rights>Springer Science+Business Media Dordrecht 2016</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c349t-60ee5e89b8eb27c7fe57350df2970252f088cde2f3da0cedfe34f6576dbaae423</citedby><cites>FETCH-LOGICAL-c349t-60ee5e89b8eb27c7fe57350df2970252f088cde2f3da0cedfe34f6576dbaae423</cites><orcidid>0000-0002-9671-2314</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/s10455-016-9502-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10455-016-9502-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Abiev, Nurlan Abievich</creatorcontrib><creatorcontrib>Nikonorov, Yuriĭ Gennadievich</creatorcontrib><title>The evolution of positively curved invariant Riemannian metrics on the Wallach spaces under the Ricci flow</title><title>Annals of global analysis and geometry</title><addtitle>Ann Glob Anal Geom</addtitle><description>This paper is devoted to the study of the evolution of positively curved metrics on the Wallach spaces
SU
(
3
)
/
T
max
,
Sp
(
3
)
/
Sp
(
1
)
×
Sp
(
1
)
×
Sp
(
1
)
, and
F
4
/
Spin
(
8
)
. We prove that for all Wallach spaces, the normalized Ricci flow evolves all generic invariant Riemannian metrics with positive sectional curvature into metrics with mixed sectional curvature. Moreover, we prove that for the spaces
Sp
(
3
)
/
Sp
(
1
)
×
Sp
(
1
)
×
Sp
(
1
)
and
F
4
/
Spin
(
8
)
, the normalized Ricci flow evolves all generic invariant Riemannian metrics with positive Ricci curvature into metrics with mixed Ricci curvature. We also get similar results for some more general homogeneous spaces.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Curvature</subject><subject>Curved</subject><subject>Differential Geometry</subject><subject>Evolution</subject><subject>Geometry</subject><subject>Global Analysis and Analysis on Manifolds</subject><subject>Invariants</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematical Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Studies</subject><subject>Texts</subject><subject>Theorems</subject><subject>Topological 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Geom</stitle><date>2016-07-01</date><risdate>2016</risdate><volume>50</volume><issue>1</issue><spage>65</spage><epage>84</epage><pages>65-84</pages><issn>0232-704X</issn><eissn>1572-9060</eissn><abstract>This paper is devoted to the study of the evolution of positively curved metrics on the Wallach spaces
SU
(
3
)
/
T
max
,
Sp
(
3
)
/
Sp
(
1
)
×
Sp
(
1
)
×
Sp
(
1
)
, and
F
4
/
Spin
(
8
)
. We prove that for all Wallach spaces, the normalized Ricci flow evolves all generic invariant Riemannian metrics with positive sectional curvature into metrics with mixed sectional curvature. Moreover, we prove that for the spaces
Sp
(
3
)
/
Sp
(
1
)
×
Sp
(
1
)
×
Sp
(
1
)
and
F
4
/
Spin
(
8
)
, the normalized Ricci flow evolves all generic invariant Riemannian metrics with positive Ricci curvature into metrics with mixed Ricci curvature. We also get similar results for some more general homogeneous spaces.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10455-016-9502-8</doi><tpages>20</tpages><orcidid>https://orcid.org/0000-0002-9671-2314</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0232-704X |
| ispartof | Annals of global analysis and geometry, 2016-07, Vol.50 (1), p.65-84 |
| issn | 0232-704X 1572-9060 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1825558350 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Algebra Analysis Curvature Curved Differential Geometry Evolution Geometry Global Analysis and Analysis on Manifolds Invariants Mathematical analysis Mathematical models Mathematical Physics Mathematics Mathematics and Statistics Studies Texts Theorems Topological manifolds |
| title | The evolution of positively curved invariant Riemannian metrics on the Wallach spaces under the Ricci flow |
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