scispace - formally typeset
Search or ask a question
Author

Jurgen Berndt

Bio: Jurgen Berndt is an academic researcher from King's College London. The author has contributed to research in topics: Symmetric space & Submanifold. The author has an hindex of 26, co-authored 84 publications receiving 2343 citations. Previous affiliations of Jurgen Berndt include University of Cologne & Stanford University.


Papers
More filters
Journal ArticleDOI
TL;DR: Olmos, Carlos Enrique, et al. this paper, this paper presented a paper on "Centro de Investigacion y Estudios de Matematica, Astronomia and Fisica" at the University of Cordoba.
Abstract: Fil: Olmos, Carlos Enrique. Universidad Nacional de Cordoba. Facultad de Matematica, Astronomia y Fisica; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Cordoba. Centro de Investigacion y Estudios de Matematica. Universidad Nacional de Cordoba. Centro de Investigacion y Estudios de Matematica; Argentina

8 citations

Journal ArticleDOI
TL;DR: In this article, the structure of real hypersurfaces with isometric Reeb flow in Kahler manifolds was investigated, and the authors classified real hyperssurfaces with Reeb flows in irreducible Hermitian s...
Abstract: We investigate the structure of real hypersurfaces with isometric Reeb flow in Kahler manifolds. As an application we classify real hypersurfaces with isometric Reeb flow in irreducible Hermitian s...

7 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied isometric cohomogeneity one actions on the (n+1)-dimensional Minkowski space up to orbit-equivalence, and they showed that there exist actions on this space which are not orbitequivalent on the complement of an n-dimensional degenerate subspace.
Abstract: We study isometric cohomogeneity one actions on the \((n+1)\)-dimensional Minkowski space \(\mathbb {L}^{n+1}\) up to orbit-equivalence. We give examples of isometric cohomogeneity one actions on \(\mathbb {L}^{n+1}\) whose orbit spaces are non-Hausdorff. We show that there exist isometric cohomogeneity one actions on \(\mathbb {L}^{n+1}\), \(n \ge 3\), which are orbit-equivalent on the complement of an n-dimensional degenerate subspace \(\mathbb {W}^n\) of \(\mathbb {L}^{n+1}\) and not orbit-equivalent on \(\mathbb {W}^n\). We classify isometric cohomogeneity one actions on \(\mathbb {L}^2\) and \(\mathbb {L}^3\) up to orbit-equivalence.

6 citations

Journal ArticleDOI
TL;DR: In this article, the radial unit vector field associated to a reflective submanifold is constructed from cohomogeneity one actions with a reflective singular orbit, which is harmonic and minimal.
Abstract: We present new examples of harmonic and minimal unit vector fields on Riemannian symmetric spaces. These examples are constructed from cohomogeneity one actions with a reflective singular orbit. The radial unit vector field associated to such a reflective submanifold is harmonic and minimal.

6 citations


Cited by
More filters
Book ChapterDOI
01 Jan 2015
TL;DR: The study of real hypersurfaces in complex projective space CP n and complex hyperbolic space CH n began at approximately the same time as Munzner's work on isoparametric hypersurface in spheres as discussed by the authors.
Abstract: The study of real hypersurfaces in complex projective space CP n and complex hyperbolic space CH n began at approximately the same time as Munzner’s work on isoparametric hypersurfaces in spheres. A key early work was Takagi’s classification [669] in 1973 of homogeneous real hypersurfaces in CP n . These hypersurfaces necessarily have constant principal curvatures, and they serve as model spaces for many subsequent classification theorems. Later Montiel [501] provided a similar list of standard examples in complex hyperbolic space CH n . In this chapter, we describe these examples of Takagi and Montiel in detail, and later we prove many important classification results involving them. We also study Hopf hypersurfaces, focal sets, parallel hypersurfaces and tubes using both standard techniques of submanifold geometry and the method of Jacobi fields.

228 citations

Journal ArticleDOI
TL;DR: In this paper, the Ricci soliton left invariant Riemannian metric is shown to be unique up to isometry and scaling, if and only if (N,g) admits a metric standard solvable extension whose corresponding standard solvmanifold is Einstein.
Abstract: We study a notion weakening the Einstein condition on a left invariant Riemannian metric g on a nilpotent Lie groupN. We consider those metrics satisfying Ric $_g=cI+D$ for some $c\in{mathbb R}$ and some derivationD of the Lie algebra ${\mathfrak n}$ ofN, where Ric $_g$ denotes the Ricci operator of $(N,g)$ . This condition is equivalent to the metric g to be a Ricci soliton. We prove that a Ricci soliton left invariant metric on N is unique up to isometry and scaling. The following characterization is also given: (N,g) is a Ricci soliton if and only if (N,g) admits a metric standard solvable extension whose corresponding standard solvmanifold $(S,\tilde{g})$ is Einstein. This gives several families of new examples of Ricci solitons. By a variational approach, we furthermore show that the Ricci soliton homogeneous nilmanifolds (N,g) are precisely the critical points of a natural functional defined on a vector space which contains all the homogeneous nilmanifolds of a given dimension as a real algebraic set.

220 citations

Book
01 Jan 2007
TL;DR: The theory of commutative spaces has been studied in the context of topological group theory as discussed by the authors, where spherical transforms and Plancherel formulae have been used.
Abstract: General theory of topological groups: Basic topological group theory Some examples Integration and convolution Representation theory and compact groups: Basic representation theory Representations of compact groups Compact Lie groups and homogeneous spaces Discrete co-compact subgroups Introduction to commutative spaces: Basic theory of commutative spaces Spherical transforms and Plancherel formulae Special case: Commutative groups Structure and analysis for commutative spaces: Riemannian symmetric spaces Weakly symmetric and reductive commutative spaces Structure of commutative nilmanifolds Analysis on commutative nilmanifolds Classification of commutative spaces Bibliography Subject index Symbol index Table index.

203 citations

Journal Article
TL;DR: In this paper, a natural generalization of harmonic maps and minimal immersions can be given by considering the functionals obtained integrating the square of the norm of the tension field or of the mean curvature vector field, respectively.
Abstract: and the corresponding Euler-Lagrange equation is H = 0, where H is the mean curvature vector field. If φ : (M, g) → (N, h) is a Riemannian immersion, then it is a critical point of the bienergy in C∞(M,N) if and only if it is a minimal immersion [26]. Thus, in order to study minimal immersions one can look at harmonic Riemannian immersions. A natural generalization of harmonic maps and minimal immersions can be given by considering the functionals obtained integrating the square of the norm of the tension field or of the mean curvature vector field, respectively. More precisely: • biharmonic maps are the critical points of the bienergy functional E2 : C∞(M,N) → R, E2(φ) = 12 ∫

178 citations