A class of Kaehler Einstein structures on the cotangent bundle

Details A class of Kaehler Einstein structures on the cotangent bundle A class of Kaehler Einstein structures on the cotangent bundle

2004-05-14

arxiv.org/abs/math/0405277v1

Mathematics

Differential Geometry

21 pages, LaTeX2e, to appear in "Publicationes Matheticae", Debrecen

Scientific paper

We use some natural lifts defined on the cotangent bundle T*M of a Riemannian manifold (M,g) in order to construct an almost Hermitian structure (G,J) of diagonal type. The obtained almost complex structure J on T*M is integrable if and only if the base manifold has constant sectional curvature and the coefficients as well as their derivatives, involved in its definition, do fulfill a certain algebraic relation. Next one obtains the condition that must be fulfilled in the case where the obtained almost Hermitian structure is almost Kaehlerian. Combining the obtained results we get a family of Kaehlerian structures on T*M, depending on two essential parameters. Next we study three conditions under which the considered Kaehlerian structures are Einstein. In one of the obtained cases we get that (T*M,G,J) has constant holomorphic curvature.

Affiliated with

Also associated with

No associations

Rating

A class of Kaehler Einstein structures on the cotangent bundle 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 A class of Kaehler Einstein structures on the cotangent bundle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A class of Kaehler Einstein structures on the cotangent bundle will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-671751