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Γενικό Σεμινάριο Μαθηματικών

  • Στοιχεία επικοινωνίαςΑ. Κοτσιώλης, Καθηγητήςemail:cotsioli AT math.upatras.gr

24.09.2008, Αίθουσα 342 κτίριο Βιολογίας/Μαθηματικών

Ημερομηνία:  Τετάρτη 24 Σεπτεμβρίου 2008

Τόπος:  Αίθουσα 342 κτίριο Βιολογίας/Μαθηματικών

Ώρα:  13:00 – 14:00 μ.μ.

Ομιλητής: Yusuke Sakane

                Osaka university, Japan

Θέμα :  Einstein metrics on compact homogeneous spaces

Περίληψη

A Riemannian manifold is called Einstein if the Ricci tensor of the metric is a multiple of itself. In case of homogeneous spaces, the Einstein equation becomes a system of non-linear algebraic equations. It is well-known that a symmetric space of compact type or an isotropy irreducible space admit an invariant Einstein metric. On the other hand, in the case that isotropy representation decomposes into more than two irreducible summands, the problem finding invariant Einstein metrics is more complicated. In 1986 Wang-Ziller discovered the first examples of compact homogeneous spaces without invariant Einstein metrics and one of these examples is a 12-dimensional homogeneous space. By a result due to Bohm and Kerr (2005), we know now that compact homogeneous spaces of 11-dimension or less admit an invariant Einstein metric.

 It is also well-known that a compact semi-simple Lie group admits an invariant Einstein metric. In 1979 D'Atri-Ziller investigated naturally reductive metrics among left invariant metrics on compact Lie groups and obtained many Einstein metrics on compact Lie groups. Then they gave a question whether there exist Einstein metrics on compact Lie groups which are not naturally reductive. In this talk we will show there exist such Einstein metrics, and discuss Einstein equations of generalized flag manifolds.

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