Kähler manifolds of quasi-constant holomorphic sectional curvatures

• Autorzy: Georgi Ganchev , Vesselka Mihova
• Języki publikacji: EN

Abstrakty

EN

The Kähler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kähler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric angle, associated with the section. A curvature identity characterizing such manifolds is found. The biconformal group of transformations whose elements transform Kähler metrics into Kähler ones is introduced and biconformal tensor invariants are obtained. This makes it possible to classify the manifolds under consideration locally. The class of locally biconformal flat Kähler metrics is shown to be exactly the class of Kähler metrics whose potential function is only a function of the distance from the origin in ℂn. Finally we show that any rotational even dimensional hypersurface carries locally a natural Kähler structure which is of quasi-constant holomorphic sectional curvatures.

Słowa kluczowe

EN

Kähler manifolds with J-invariant distributions; Kähler manifolds of quasi-constant holomorphic sectional curvatures; biconformal transformations; biconformal invariants; even dimensional rotational hypersurfaces

Kategorie tematyczne

• 52C25: Rigidity and flexibility of structures
• 53B20: Local Riemannian geometry

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 1
• Strony: 43-75

Daty

wydano

2008-03-01

online

2008-02-26

Twórcy

autor

Georgi Ganchev

• Bulgarian Academy of Sciences

autor

Vesselka Mihova

• University of Sofia

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-008-0004-1