Displaying similar documents to “Geometric structures on manifolds and holonomy-invariant metrics.”

On naturally reductive left-invariant metrics of SL ( 2 , ℝ )

Stefan Halverscheid, Andrea Iannuzzi (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On any real semisimple Lie group we consider a one-parameter family of left-invariant naturally reductive metrics. Their geodesic flow in terms of Killing curves, the Levi Civita connection and the main curvature properties are explicitly computed. Furthermore we present a group theoretical revisitation of a classical realization of all simply connected 3-dimensional manifolds with a transitive group of isometries due to L. Bianchi and É. Cartan. As a consequence one obtains a characterization...

Isospectral deformations of closed riemannian manifolds with different scalar curvature

Carolyn S. Gordon, Ruth Gornet, Dorothee Schueth, David L. Webb, Edward N. Wilson (1998)

Annales de l'institut Fourier

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We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds , more precisely, on S n × T m , where T m is a torus of dimension m ≥ 2 and S n is a sphere of dimension n ≥ 4 . These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.

Generalized Kählerian manifolds and transformation of generalized contact structures

Habib Bouzir, Gherici Beldjilali, Mohamed Belkhelfa, Aissa Wade (2017)

Archivum Mathematicum

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The aim of this paper is two-fold. First, new generalized Kähler manifolds are constructed starting from both classical almost contact metric and almost Kählerian manifolds. Second, the transformation construction on classical Riemannian manifolds is extended to the generalized geometry setting.

Harmonic maps and Riemannian submersions between manifolds endowed with special structures

Stere Ianuş, Gabriel Eduard Vîlcu, Rodica Cristina Voicu (2011)

Banach Center Publications

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It is well known that Riemannian submersions are of interest in physics, owing to their applications in the Yang-Mills theory, Kaluza-Klein theory, supergravity and superstring theories. In this paper we give a survey of harmonic maps and Riemannian submersions between manifolds equipped with certain geometrical structures such as almost Hermitian structures, contact structures, f-structures and quaternionic structures. We also present some new results concerning holomorphic maps and...