# Kähler manifolds of quasi-constant holomorphic sectional curvatures

Georgi Ganchev; Vesselka Mihova

Open Mathematics (2008)

- Volume: 6, Issue: 1, page 43-75
- ISSN: 2391-5455

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topGeorgi Ganchev, and Vesselka Mihova. "Kähler manifolds of quasi-constant holomorphic sectional curvatures." Open Mathematics 6.1 (2008): 43-75. <http://eudml.org/doc/269588>.

@article{GeorgiGanchev2008,

abstract = {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.},

author = {Georgi Ganchev, Vesselka Mihova},

journal = {Open Mathematics},

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

language = {eng},

number = {1},

pages = {43-75},

title = {Kähler manifolds of quasi-constant holomorphic sectional curvatures},

url = {http://eudml.org/doc/269588},

volume = {6},

year = {2008},

}

TY - JOUR

AU - Georgi Ganchev

AU - Vesselka Mihova

TI - Kähler manifolds of quasi-constant holomorphic sectional curvatures

JO - Open Mathematics

PY - 2008

VL - 6

IS - 1

SP - 43

EP - 75

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/269588

ER -

## References

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