Peter Quast

MAXIMAL TORI OF EXTRINSIC SYMMETRIC SPACES AND MERIDIANS

We give a different proof of a theorem of O. Loos [5] which char acterizes maximal tori of extrinsically symmetric spaces. On the way we sh ow some facts on certain symmetric subspaces, so called meridians, which previ ously have been known only using classification.

Pluriharmonic maps into Kähler symmetric spaces and Sym’s formula

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Pluriharmonic maps into outer symmetric spaces and a subdivision of Weyl chambers

-structures are weak forms of multiplications on closed oriented manifolds. As shown by Hopf the rational cohomology algebras of manifolds admitting

The spectral parameter of pluriharmonic maps

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ON SOME SPACES OF MINIMAL GEODESICS IN RIEMANNIAN SYMMETRIC SPACES

-structures are free over odd degree generators. We prove that this condition is also sufficient for the existence of

CONVEXITY OF REFLECTIVE SUBMANIFOLDS IN SYMMETRIC

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R

-structures on manifolds which are nilpotent in the sense of homotopy theory. This includes homogeneous spaces with connected isotropy groups. Passing to a more geometric perspective we show that on compact oriented Riemannian symmetric spaces with connected isotropy groups and free rational cohomology algebras the canonical products given by geodesic symmetries define

-SPACES

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Twistor fibrations over Hermitian symmetric spaces and harmonic maps

-structures. This extends work of Albers, Frauenfelder and Solomon on