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We investigate the submanifold geometry of the orbits of Hermann actions on Riemannian symmetric spaces. After proving that the curvature and shape operators of these orbits commute , we calculate the eigenvalues of the shape operators in terms of the restricted roots. As applications, we get a formula for the volumes of the orbits and a new proof of a… (More)

Uhlenbeck proved that a set of simple elements generates the group of rational loops in GL(n, C) that satisfy the U(n)-reality condition. For an arbitrary complex reductive group, a choice of representation defines a notion of rationality and enables us to write down a natural set of simple elements. Using these simple elements we prove generator theorems… (More)

- O Goertsches
- 2006

Motivated by Zirnbauer [Zir 1996], we develop a theory of Riemannian supermanifolds up to a definition of Riemannian symmetric superspaces. Various fundamental concepts needed for the study of these spaces both from the Riemannian and the Lie theoretical viewpoint are introduced, e.g. geodesics, isometry groups and invariant metrics on Lie supergroups and… (More)

- Oliver Goertsches, Eckhard Meinrenken
- 2012

We show that for every symmetric space G/K of compact type with K connected, the K-action on G/K by left translations is equivariantly formal.

We investigate left-invariant Hitchin and hypo flows on 5-, 6-and 7-dimensional Lie groups. They provide Riemannian cohomogeneity-one man-ifolds of one dimension higher with holonomy contained in SU(3), G 2 and Spin(7), respectively, which are in general geodesically incomplete. Generalizing results of Conti, we prove that for large classes of solvable Lie… (More)

- Oliver Goertsches, Gudlaugur Thorbergsson
- 2007

We investigate the submanifold geometry of the orbits of Hermann actions on Riemannian symmetric spaces. After proving that the curvature and shape operators of these orbits commute , we calculate the eigenvalues of the shape operators in terms of the restricted roots. As applications, we get a formula for the volumes of the orbits and a new proof of a… (More)

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