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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...

Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

Rafael López, Esma Demir (2014)

Open Mathematics

We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.

Hermitian curvature flow

Jeffrey Streets, Gang Tian (2011)

Journal of the European Mathematical Society

We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler–Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler–Einstein metrics, and are automatically Kähler–Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existence and regularity results for this flow, as well as stability for the flow near Kähler–Einstein metrics...

Hermitian Manifolds of Pointwise Constant Antiholomorphic Sectional Curvatures

Ganchev, Georgi, Kassabov, Ognian (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 53B35, Secondary 53C50.In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.

Currently displaying 2861 – 2880 of 8747