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Harmonie reflections

Lieven Vanhecke, Maria-Elena Vazquez-Abal (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study local reflections ϕ σ with respect to a curve σ in a Riemannian manifold and prove that σ is a geodesic if ϕ σ is a harmonic map. Moreover, we prove that the Riemannian manifold has constant curvature if and only if ϕ σ is harmonic for all geodesies σ .

Hasse diagrams for parabolic geometries

Krump, Lukáš, Souček, Vladimír (2003)

Proceedings of the 22nd Winter School "Geometry and Physics"

The invariant differential operators on a manifold with a given parabolic structure come in two classes, standard and non-standard, and can be further subdivided into regular and singular ones. The standard regular operators come in repeated patterns, the Bernstein-Gelfand-Gelfand sequences, described by Hasse diagrams. In this paper, the authors present an alternative characterization of Hasse diagrams, which is quite efficient in the case of low gradings. Several examples are given.

H-conformal anti-invariant submersions from almost quaternionic Hermitian manifolds

Kwang Soon Park (2020)

Czechoslovak Mathematical Journal

We introduce the notions of h-conformal anti-invariant submersions and h-conformal Lagrangian submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, anti-invariant submersions, h-anti-invariant submersions, h-Lagrangian submersion, conformal anti-invariant submersions. We investigate their properties: the integrability of distributions, the geometry of foliations, the conditions for such...

Heat flows for extremal Kähler metrics

Santiago R. Simanca (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let ( M , J , Ω ) be a closed polarized complex manifold of Kähler type. Let G be the maximal compact subgroup of the automorphism group of ( M , J ) . On the space of Kähler metrics that are invariant under G and represent the cohomology class Ω , we define a flow equation whose critical points are the extremal metrics,i.e.those that minimize the square of the L 2 -norm of the scalar curvature. We prove that the dynamical system in this space of metrics defined by the said flow does not have periodic orbits, and that its...

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