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A property of Wallach's flag manifolds

Teresa Arias-Marco (2007)

Archivum Mathematicum

In this note we study the Ledger conditions on the families of flag manifold ( M 6 = S U ( 3 ) / S U ( 1 ) × S U ( 1 ) × S U ( 1 ) , g ( c 1 , c 2 , c 3 ) ) , ( M 12 = S p ( 3 ) / S U ( 2 ) × S U ( 2 ) × S U ( 2 ) , g ( c 1 , c 2 , c 3 ) ) , constructed by N. R. Wallach in (Wallach, N. R., Compact homogeneous Riemannian manifols with strictly positive curvature, Ann. of Math. 96 (1972), 276–293.). In both cases, we conclude that every member of the both families of Riemannian flag manifolds is a D’Atri space if and only if it is naturally reductive. Therefore, we finish the study of M 6 made by D’Atri and Nickerson in (D’Atri, J. E., Nickerson, H. K., Geodesic...

A quantum Duistermaat-Heckamn formula?

Alberto Ibort (2003)

RACSAM

Some aspects of Duistermaat-Heckman formula in finite dimensions are reviewed. We especulate with some of its possible extensions to infinite dimensions. In particular we review the localization principle and the geometry of loop spaces following Witten and Atiyah?s insight.

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