Twistor geometry and warped product orthogonal complex structures
نویسندگان
چکیده
منابع مشابه
On the Complex Geometry of Twistor Spaces
In the rst part of this note we present a brief account of some recent results which have been obtained by several authors using twistor techniques. They are mainly concerned with bimeromorphic properties of complex manifolds. In the second half we concentrate on twistor spaces of anti-self-dual complex surfaces. Following Tsanov Ts] and thanks to some recent joint work with Kim and LeBrun KP]]...
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— Let M be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space Z admits a natural metric. The aim of this article is to study properties of complex structures on Z which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on M (scalar flat, scalar-flat Kähler...) in terms of complex properties of it...
متن کاملCompatible Complex Structures on Twistor Spaces
Let (M, g) be an oriented 4-dimensional Riemannian manifold (not necessarily compact). Due to the Hodge-star operator ⋆, we have a decomposition of the bivector bundle ∧2 TM = ∧+ ⊕ ∧− . Here ∧± is the eigen-subbundle for the eigenvalue ±1 of ⋆. The metric g on M induces a metric, denoted by < , >, on the bundle ∧2 TM . Let π : Z = S (∧+) −→ M be the sphere bundle; the fiber over a point m ∈ M p...
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Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...
متن کاملSpectral Geometry of Harmonic Maps into Warped Product Manifolds Ii
Let (Mn,g) be a closed Riemannian manifold and N a warped product manifold of two space forms. We investigate geometric properties by the spectra of the Jacobi operator of a harmonic map φ : M → N . In particular, we show if N is a warped product manifold of Euclidean space with a space form and φ,ψ : M → N are two projectively harmonic maps, then the energy of φ and ψ are equal up to constant ...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2011
ISSN: 0012-7094
DOI: 10.1215/00127094-2010-068