A class of Kaehler Einstein structures on the cotangent bundle
We use some natural lifts defined on the cotangent bundle T*M of a Riemannian manifold (M,g) in order to construct an almost Hermitian structure (G,J) of diagonal type. The obtained almost complex structure J on T*M is integrable if and only if the base manifold has constant sectional curvature and...
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| creator | Oproiu, Vasile Porosniuc, Dumitru Daniel |
| description | We use some natural lifts defined on the cotangent bundle T*M of a Riemannian
manifold (M,g) in order to construct an almost Hermitian structure (G,J) of
diagonal type. The obtained almost complex structure J on T*M is integrable if
and only if the base manifold has constant sectional curvature and the
coefficients as well as their derivatives, involved in its definition, do
fulfill a certain algebraic relation. Next one obtains the condition that must
be fulfilled in the case where the obtained almost Hermitian structure is
almost Kaehlerian. Combining the obtained results we get a family of Kaehlerian
structures on T*M, depending on two essential parameters. Next we study three
conditions under which the considered Kaehlerian structures are Einstein. In
one of the obtained cases we get that (T*M,G,J) has constant holomorphic
curvature. |
| doi_str_mv | 10.48550/arxiv.math/0405277 |
| format | Article |
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manifold (M,g) in order to construct an almost Hermitian structure (G,J) of
diagonal type. The obtained almost complex structure J on T*M is integrable if
and only if the base manifold has constant sectional curvature and the
coefficients as well as their derivatives, involved in its definition, do
fulfill a certain algebraic relation. Next one obtains the condition that must
be fulfilled in the case where the obtained almost Hermitian structure is
almost Kaehlerian. Combining the obtained results we get a family of Kaehlerian
structures on T*M, depending on two essential parameters. Next we study three
conditions under which the considered Kaehlerian structures are Einstein. In
one of the obtained cases we get that (T*M,G,J) has constant holomorphic
curvature.</description><identifier>DOI: 10.48550/arxiv.math/0405277</identifier><language>eng</language><subject>Mathematics - Differential Geometry</subject><creationdate>2004-05</creationdate><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/math/0405277$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.math/0405277$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Oproiu, Vasile</creatorcontrib><creatorcontrib>Porosniuc, Dumitru Daniel</creatorcontrib><title>A class of Kaehler Einstein structures on the cotangent bundle</title><description>We use some natural lifts defined on the cotangent bundle T*M of a Riemannian
manifold (M,g) in order to construct an almost Hermitian structure (G,J) of
diagonal type. The obtained almost complex structure J on T*M is integrable if
and only if the base manifold has constant sectional curvature and the
coefficients as well as their derivatives, involved in its definition, do
fulfill a certain algebraic relation. Next one obtains the condition that must
be fulfilled in the case where the obtained almost Hermitian structure is
almost Kaehlerian. Combining the obtained results we get a family of Kaehlerian
structures on T*M, depending on two essential parameters. Next we study three
conditions under which the considered Kaehlerian structures are Einstein. In
one of the obtained cases we get that (T*M,G,J) has constant holomorphic
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manifold (M,g) in order to construct an almost Hermitian structure (G,J) of
diagonal type. The obtained almost complex structure J on T*M is integrable if
and only if the base manifold has constant sectional curvature and the
coefficients as well as their derivatives, involved in its definition, do
fulfill a certain algebraic relation. Next one obtains the condition that must
be fulfilled in the case where the obtained almost Hermitian structure is
almost Kaehlerian. Combining the obtained results we get a family of Kaehlerian
structures on T*M, depending on two essential parameters. Next we study three
conditions under which the considered Kaehlerian structures are Einstein. In
one of the obtained cases we get that (T*M,G,J) has constant holomorphic
curvature.</abstract><doi>10.48550/arxiv.math/0405277</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Differential Geometry |
| title | A class of Kaehler Einstein structures on the cotangent bundle |
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