Lectures on Kähler Geometry

Moroianu, Andrei

doi:10.1017/cbo9780511618666

Cited by 102 publications

(115 citation statements)

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“…∇ω = 0, ∇g = 0, ∇J = 0) and its torsion satisfies The Chern-Ricci form is always closed and locally p = dθ, where θ is the 1-form given by (M, J), where c 1 (M, J) ∈ H 2 (M, R) is the first Chern class (see e.g. [M,Chapter 16] or [KN,Chapter 12] for further information).…”

Section: Appendix: Chern-ricci Formmentioning

confidence: 99%

Curvature flows for almost-hermitian Lie groups

Lauret¹

2014

Trans. Amer. Math. Soc.

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Abstract. We study curvature flows in the locally homogeneous case (e.g. compact quotients of Lie groups, solvmanifolds, nilmanifolds) in a unified way, by considering a generic flow under just a few natural conditions on the broad class of almost-hermitian structures. As a main tool, we use an ODE system defined on the variety of 2n-dimensional Lie algebras, called the bracket flow, whose solutions differ from those to the original curvature flow by only pull-back by time-dependent diffeomorphisms. The approach, which has already been used to study the Ricci flow on homogeneous manifolds, is useful to better visualize the possible pointed limits of solutions, under diverse rescalings, as well as to address regularity issues. Immortal, ancient and self-similar solutions arise naturally from the qualitative analysis of the bracket flow. The Chern-Ricci flow and the symplectic curvature flow are considered in more detail.

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Section: Appendix: Chern-ricci Formmentioning

confidence: 99%

Curvature flows for almost-hermitian Lie groups

Lauret¹

2014

Trans. Amer. Math. Soc.

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“…The Ricci tensor built out of the metric g µν * For an introduction to Hermitian structures and complex differential geometry, see e.g. [48]. is denoted as R µν .…”

Section: Action and Field Equations For N Real Scalarsmentioning

confidence: 99%

Tensor-multi-scalar theories: relativistic stars and 3 + 1 decomposition

Horbatsch

Silva

Gerosa

et al. 2015

Class. Quantum Grav.

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Abstract. Gravitational theories with multiple scalar fields coupled to the metric and each other -a natural extension of the well studied single-scalar-tensor theories -are interesting phenomenological frameworks to describe deviations from general relativity in the strong-field regime. In these theories, the N -tuple of scalar fields takes values in a coordinate patch of an N -dimensional Riemannian target-space manifold whose properties are poorly constrained by weak-field observations. Here we introduce for simplicity a non-trivial model with two scalar fields and a maximally symmetric target-space manifold. Within this model we present a preliminary investigation of spontaneous scalarization for relativistic, perfect fluid stellar models in spherical symmetry. We find that the scalarization threshold is determined by the eigenvalues of a symmetric scalar-matter coupling matrix, and that the properties of strongly scalarized stellar configurations additionally depend on the targetspace curvature radius. In preparation for numerical relativity simulations, we also write down the 3 + 1 decomposition of the field equations for generic tensor-multi-scalar theories.

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“…On a Kähler compact manifold every Killing vector field is holomorphic (see [14]). Thus, ξ ∈ hol(M, J ).…”

Section: Proposition 31 Let (M J ) Be a Compact Complex Manifold Wimentioning

confidence: 99%

Compact conformally Kähler Einstein-Weyl manifolds

Jelonek

2012

Ann Glob Anal Geom

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We give a description of compact conformally Kähler Einstein-Weyl manifolds whose Ricci tensor is Hermitian. IntroductionIn this paper we shall investigate compact Einstein-Weyl structures (M, [g], D) on a complex manifold (M, J ), dimM ≥ 4, which are conformally Kähler and whose Ricci tensor ρ D is Hermitian, i.e., ρ D is J -invariant.We give a complete classification of compact Einstein-Weyl structures

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Lectures on Kähler Geometry

Abstract: These lecture notes, based on a graduate course given by the author at Hamburg University in the Autumn of 2003, were withdrawn from the preprint server because of copyright constraints.They will be available soon as graduate textbook.

Cited by 102 publications

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Curvature flows for almost-hermitian Lie groups

Curvature flows for almost-hermitian Lie groups

Tensor-multi-scalar theories: relativistic stars and 3 + 1 decomposition

Compact conformally Kähler Einstein-Weyl manifolds

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