Kaehler Manifolds of Quasi-Constant Holomorphic Sectional Curvatures

Details Kaehler Manifolds of Quasi-Constant Holomorphic Sectional Curvatures Kaehler Manifolds of Quasi-Constant Holomorphic Sectional Curvatures

2005-05-31

arxiv.org/abs/math/0505671v1

Cent. Eur. J. Math., 6 (2008) 1, 43-75.

Mathematics

Differential Geometry

36 pages

Scientific paper

10.2478/s11533-008-0004-1

The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler 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 Kaehler metrics into Kaehler 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 Kaehler metrics is shown to be exactly the class of Kaehler metrics whose potential function is only a function of the distance from the origin in complex Euclidean space. Finally we show that any rotational even dimensional hypersurface carries locally a natural Kaehler structure, which is of quasi-constant holomorphic sectional curvatures.

Affiliated with

Also associated with

No associations

Rating

Kaehler Manifolds of Quasi-Constant Holomorphic Sectional Curvatures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Kaehler Manifolds of Quasi-Constant Holomorphic Sectional Curvatures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Kaehler Manifolds of Quasi-Constant Holomorphic Sectional Curvatures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-455697