Showing papers by "Jurgen Berndt published in 2013"
TL;DR: In this article, the existence of real hypersurfaces with isometric Reeb flow in the complex quadrics Qm = SOm+2/SOmSO2, m ≥ 3.
Abstract: We classify real hypersurfaces with isometric Reeb flow in the complex quadrics Qm = SOm+2/SOmSO2, m ≥ 3. We show that m is even, say m = 2k, and any such hypersurface is an open part of a tube around a k-dimensional complex projective space ℂPk which is embedded canonically in Q2k as a totally geodesic complex submanifold. As a consequence, we get the non-existence of real hypersurfaces with isometric Reeb flow in odd-dimensional complex quadrics Q2k+1, k ≥ 1. To our knowledge the odd-dimensional complex quadrics are the first examples of homogeneous Kahler manifolds which do not admit a real hypersurface with isometric Reeb flow.
64 citations
TL;DR: In this paper, a conceptual approach to the classification of cohomogeneity one actions on Riemannian symmetric spaces of noncompact type in terms of orbit equivalence was developed.
Abstract: An isometric action of a Lie group on a Riemannian manifold is of cohomogeneity one if the corresponding orbit space is one-dimensional. In this article we develop a conceptual approach to the classification of cohomogeneity one actions on Riemannian symmetric spaces of noncompact type in terms of orbit equivalence. As a consequence, we find many new examples of cohomogeneity one actions on Riemannian symmetric spaces of noncompact type. We apply our conceptual approach to derive explicit classifications of cohomogeneity one actions on some symmetric spaces.
42 citations
TL;DR: In this article, the authors classify certain contact hypersurfaces in the Riemannian symmetric space SU2,m/S(U2Um), m ≥ 3.
Abstract: In this paper, we classify certain contact hypersurfaces in the Riemannian symmetric space SU2,m/S(U2Um), m ≥ 3.
15 citations
TL;DR: In this paper, the polar actions on the complex hyperbolic plane up to orbit equivalence were classified and five polar actions of cohomogeneity 1 and four polar actions were defined.
Abstract: We classify the polar actions on the complex hyperbolic plane \({\mathbb{C} H^2}\) up to orbit equivalence. Apart from the trivial and transitive polar actions, there are five polar actions of cohomogeneity 1 and four polar actions of cohomogeneity 2.
11 citations
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TL;DR: In this article, a general structure theory for compact homogeneous Riemannian manifolds in relation to the co-index of symmetry is developed, which can be used to classify irreducible, simply connected, compact homogenous RiemANNIAN manifolds whose coindex is less or equal than three.
Abstract: We develop a general structure theory for compact homogeneous Riemannian manifolds in relation to the co-index of symmetry. We will then use these results to classify irreducible, simply connected, compact homogeneous Riemannian manifolds whose co-index of symmetry is less or equal than three. We will also construct many examples which arise from the theory of polars and centrioles in Riemannian symmetric spaces of compact type.
9 citations
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TL;DR: In this article, the authors carried out a systematic study of contact hypersurfaces in Kaehler manifolds and applied these general results to obtain classifications of contact surfaces with constant mean curvature in the complex quadric SO(n+2)/SO(n)SO(2) and its noncompact dual space for n > 2.
Abstract: A contact hypersurface in a Kaehler manifold is a real hypersurface for which the induced almost contact metric structure determines a contact structure. We carry out a systematic study of contact hypersurfaces in Kaehler manifolds. We then apply these general results to obtain classifications of contact hypersurfaces with constant mean curvature in the complex quadric SO(n+2)/SO(n)SO(2) and its noncompact dual space SO(n,2)/SO(n)SO(2) for n > 2.
3 citations
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TL;DR: In this article, it was shown that real hypersurfaces with isometric Reeb flow in complex quadrics are not even, say m = 2k, and any such hypersurface is an open part of a tube around a k-dimensional complex projective space, which is embedded canonically in Q^{2k} as a totally geodesic complex submanifold.
Abstract: We classify real hypersurfaces with isometric Reeb flow in the complex quadrics Q^m for m > 2. We show that m is even, say m = 2k, and any such hypersurface is an open part of a tube around a k-dimensional complex projective space CP^k which is embedded canonically in Q^{2k} as a totally geodesic complex submanifold. As a consequence we get the non-existence of real hypersurfaces with isometric Reeb flow in odd-dimensional complex quadrics.
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TL;DR: In this article, the cohomogeneity one actions on the noncompact duals of the symmetric spaces G_2, SU_3 and the real oriented two-plane Grassmannians are classified up to orbit equivalence.
Abstract: We classify, up to orbit equivalence, the cohomogeneity one actions on the noncompact duals of the symmetric spaces G_2, SU_3 and the real oriented two-plane Grassmannians.