Classification of generalized normal homogeneous Riemannian manifolds of positive Euler characteristic
The authors give a short survey of previous results on generalized normal homogeneous ( δ-homogeneous, in other terms) Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with nonnegative sectional curvature, which properly includes the class of all normal homogeneous Rieman...
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| Veröffentlicht in: | Differential geometry and its applications 2011-08, Vol.29 (4), p.533-546 |
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| creator | Berestovskiĭ, V.N. Nikitenko, E.V. Nikonorov, Yu.G. |
| description | The authors give a short survey of previous results on generalized normal homogeneous (
δ-homogeneous, in other terms) Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with nonnegative sectional curvature, which properly includes the class of all normal homogeneous Riemannian manifolds. As a continuation and an application of these results, they prove that the family of all compact simply connected indecomposable generalized normal homogeneous Riemannian manifolds with positive Euler characteristic, which are not normal homogeneous, consists exactly of all generalized flag manifolds
Sp
(
l
)
/
U
(
1
)
⋅
Sp
(
l
−
1
)
=
C
P
2
l
−
1
,
l
⩾
2
, supplied with invariant Riemannian metrics of positive sectional curvature with the pinching constants (the ratio of the minimal sectional curvature to the maximal one) in the open interval
(
1
/
16
,
1
/
4
)
. This implies very unusual geometric properties of the adjoint representation of
Sp
(
l
)
,
l
⩾
2
. Some unsolved questions are suggested. |
| doi_str_mv | 10.1016/j.difgeo.2011.04.032 |
| format | Article |
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δ-homogeneous, in other terms) Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with nonnegative sectional curvature, which properly includes the class of all normal homogeneous Riemannian manifolds. As a continuation and an application of these results, they prove that the family of all compact simply connected indecomposable generalized normal homogeneous Riemannian manifolds with positive Euler characteristic, which are not normal homogeneous, consists exactly of all generalized flag manifolds
Sp
(
l
)
/
U
(
1
)
⋅
Sp
(
l
−
1
)
=
C
P
2
l
−
1
,
l
⩾
2
, supplied with invariant Riemannian metrics of positive sectional curvature with the pinching constants (the ratio of the minimal sectional curvature to the maximal one) in the open interval
(
1
/
16
,
1
/
4
)
. This implies very unusual geometric properties of the adjoint representation of
Sp
(
l
)
,
l
⩾
2
. Some unsolved questions are suggested.</description><identifier>ISSN: 0926-2245</identifier><identifier>EISSN: 1872-6984</identifier><identifier>DOI: 10.1016/j.difgeo.2011.04.032</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Classification ; Clifford–Wolf homogeneous Riemannian manifolds ; Clifford–Wolf translations ; Constants ; Curvature ; G.o. spaces ; Generalized normal homogeneous Riemannian manifolds ; Geodesics ; Homogeneous spaces ; Homogeneous spaces of positive Euler characteristic ; Invariants ; Manifolds ; Mathematical analysis ; Normal homogeneous Riemannian manifolds ; Orbits ; δ-Homogeneous Riemannian manifolds</subject><ispartof>Differential geometry and its applications, 2011-08, Vol.29 (4), p.533-546</ispartof><rights>2011 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c384t-1b7e5e67d04364fdd643817ccf6158a999cfc5af70885785dd1a24d7c7c9fa523</citedby><cites>FETCH-LOGICAL-c384t-1b7e5e67d04364fdd643817ccf6158a999cfc5af70885785dd1a24d7c7c9fa523</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.difgeo.2011.04.032$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Berestovskiĭ, V.N.</creatorcontrib><creatorcontrib>Nikitenko, E.V.</creatorcontrib><creatorcontrib>Nikonorov, Yu.G.</creatorcontrib><title>Classification of generalized normal homogeneous Riemannian manifolds of positive Euler characteristic</title><title>Differential geometry and its applications</title><description>The authors give a short survey of previous results on generalized normal homogeneous (
δ-homogeneous, in other terms) Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with nonnegative sectional curvature, which properly includes the class of all normal homogeneous Riemannian manifolds. As a continuation and an application of these results, they prove that the family of all compact simply connected indecomposable generalized normal homogeneous Riemannian manifolds with positive Euler characteristic, which are not normal homogeneous, consists exactly of all generalized flag manifolds
Sp
(
l
)
/
U
(
1
)
⋅
Sp
(
l
−
1
)
=
C
P
2
l
−
1
,
l
⩾
2
, supplied with invariant Riemannian metrics of positive sectional curvature with the pinching constants (the ratio of the minimal sectional curvature to the maximal one) in the open interval
(
1
/
16
,
1
/
4
)
. This implies very unusual geometric properties of the adjoint representation of
Sp
(
l
)
,
l
⩾
2
. Some unsolved questions are suggested.</description><subject>Classification</subject><subject>Clifford–Wolf homogeneous Riemannian manifolds</subject><subject>Clifford–Wolf translations</subject><subject>Constants</subject><subject>Curvature</subject><subject>G.o. spaces</subject><subject>Generalized normal homogeneous Riemannian manifolds</subject><subject>Geodesics</subject><subject>Homogeneous spaces</subject><subject>Homogeneous spaces of positive Euler characteristic</subject><subject>Invariants</subject><subject>Manifolds</subject><subject>Mathematical analysis</subject><subject>Normal homogeneous Riemannian manifolds</subject><subject>Orbits</subject><subject>δ-Homogeneous Riemannian manifolds</subject><issn>0926-2245</issn><issn>1872-6984</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LxDAUxIMouK5-Aw-9eWpN0rRJL4Is6x9YEETPISYvu29pmzXpLuint3U9exoYZob3foRcM1owyurbbeHQryEUnDJWUFHQkp-QGVOS53WjxCmZ0YbXOeeiOicXKW0pZbwRfEb8ojUpoUdrBgx9Fny2hh6iafEbXNaH2Jk224QuTHbYp-wVoTN9j6bPRkUfWpem2i4kHPAA2XLfQszsxkRjB4iYBrSX5MybNsHVn87J-8PybfGUr14enxf3q9yWSgw5-5BQQS0dFWUtvHO1KBWT1vqaVco0TWO9rYyXVKlKqso5Zrhw0krbeFPxck5ujru7GD73kAbdYbLQtub3eK2ampeMcTEmxTFpY0gpgte7iJ2JX5pRPVHVW32kqieqmgo9Uh1rd8cajF8cEKJOFqG34DCCHbQL-P_AD2sShMg</recordid><startdate>20110801</startdate><enddate>20110801</enddate><creator>Berestovskiĭ, V.N.</creator><creator>Nikitenko, E.V.</creator><creator>Nikonorov, Yu.G.</creator><general>Elsevier B.V</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20110801</creationdate><title>Classification of generalized normal homogeneous Riemannian manifolds of positive Euler characteristic</title><author>Berestovskiĭ, V.N. ; Nikitenko, E.V. ; Nikonorov, Yu.G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c384t-1b7e5e67d04364fdd643817ccf6158a999cfc5af70885785dd1a24d7c7c9fa523</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Classification</topic><topic>Clifford–Wolf homogeneous Riemannian manifolds</topic><topic>Clifford–Wolf translations</topic><topic>Constants</topic><topic>Curvature</topic><topic>G.o. spaces</topic><topic>Generalized normal homogeneous Riemannian manifolds</topic><topic>Geodesics</topic><topic>Homogeneous spaces</topic><topic>Homogeneous spaces of positive Euler characteristic</topic><topic>Invariants</topic><topic>Manifolds</topic><topic>Mathematical analysis</topic><topic>Normal homogeneous Riemannian manifolds</topic><topic>Orbits</topic><topic>δ-Homogeneous Riemannian manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Berestovskiĭ, V.N.</creatorcontrib><creatorcontrib>Nikitenko, E.V.</creatorcontrib><creatorcontrib>Nikonorov, Yu.G.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</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>Differential geometry and its applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Berestovskiĭ, V.N.</au><au>Nikitenko, E.V.</au><au>Nikonorov, Yu.G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Classification of generalized normal homogeneous Riemannian manifolds of positive Euler characteristic</atitle><jtitle>Differential geometry and its applications</jtitle><date>2011-08-01</date><risdate>2011</risdate><volume>29</volume><issue>4</issue><spage>533</spage><epage>546</epage><pages>533-546</pages><issn>0926-2245</issn><eissn>1872-6984</eissn><abstract>The authors give a short survey of previous results on generalized normal homogeneous (
δ-homogeneous, in other terms) Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with nonnegative sectional curvature, which properly includes the class of all normal homogeneous Riemannian manifolds. As a continuation and an application of these results, they prove that the family of all compact simply connected indecomposable generalized normal homogeneous Riemannian manifolds with positive Euler characteristic, which are not normal homogeneous, consists exactly of all generalized flag manifolds
Sp
(
l
)
/
U
(
1
)
⋅
Sp
(
l
−
1
)
=
C
P
2
l
−
1
,
l
⩾
2
, supplied with invariant Riemannian metrics of positive sectional curvature with the pinching constants (the ratio of the minimal sectional curvature to the maximal one) in the open interval
(
1
/
16
,
1
/
4
)
. This implies very unusual geometric properties of the adjoint representation of
Sp
(
l
)
,
l
⩾
2
. Some unsolved questions are suggested.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.difgeo.2011.04.032</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0926-2245 |
| ispartof | Differential geometry and its applications, 2011-08, Vol.29 (4), p.533-546 |
| issn | 0926-2245 1872-6984 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_896231124 |
| source | ScienceDirect Journals (5 years ago - present); EZB-FREE-00999 freely available EZB journals |
| subjects | Classification Clifford–Wolf homogeneous Riemannian manifolds Clifford–Wolf translations Constants Curvature G.o. spaces Generalized normal homogeneous Riemannian manifolds Geodesics Homogeneous spaces Homogeneous spaces of positive Euler characteristic Invariants Manifolds Mathematical analysis Normal homogeneous Riemannian manifolds Orbits δ-Homogeneous Riemannian manifolds |
| title | Classification of generalized normal homogeneous Riemannian manifolds of positive Euler characteristic |
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