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INVARIANT EINSTEIN METRICS ON GENERALIZED FLAG MANIFOLDS WITH TWO ISOTROPY SUMMANDS

Part of: Global differential geometry Lie groups

Published online by Cambridge University Press:  19 July 2011

ANDREAS ARVANITOYEORGOS  and
IOANNIS CHRYSIKOS
ANDREAS ARVANITOYEORGOS
Affiliation:
Department of Mathematics, University of Patras, GR-26500 Rion, Greece (email: arvanito@math.upatras.gr)
IOANNIS CHRYSIKOS*
Affiliation:
Department of Mathematics, University of Patras, GR-26500 Rion, Greece (email: xrysikos@master.math.upatras.gr)
*
✉For correspondence; e-mail: xrysikos@master.math.upatras.gr
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Abstract

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Let M=G/K be a generalized flag manifold, that is, an adjoint orbit of a compact, connected and semisimple Lie group G. We use a variational approach to find non-Kähler homogeneous Einstein metrics for flag manifolds with two isotropy summands. We also determine the nature of these Einstein metrics as critical points of the scalar curvature functional under fixed volume.

Keywords

Einstein manifoldhomogeneous spacegeneralized flag manifoldisotropy representationhighest weightWeyl’s formulabordered Hessian

MSC classification

Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 22E46: Semisimple Lie groups and their representations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 90 , Issue 2 , April 2011 , pp. 237 - 251
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The authors were partially supported by C. Carathéodory grant number C.161 2007-10, University of Patras.

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