On the geometry of Kähler-Poisson structures

Details On the geometry of Kähler-Poisson structures On the geometry of Kähler-Poisson structures

2011-03-30

arxiv.org/abs/1103.5862v1

Mathematics

Differential Geometry

Scientific paper

We prove that the Riemannian geometry of almost K\"ahler submanifolds can be expressed in terms of the Poisson algebra of smooth functions on the manifold. Subsequently, K\"ahler-Poisson algebras are introduced, and it is shown that a purely algebraic theory of geometry and curvature can be developed. As an illustration of the new concepts we show that if the sectional curvature is independent of the choice of tangent plane, then it Poisson commutes with all elements in the algebra, and prove that a bound on the Ricci curvature induces a bound on the eigenvalues of the Laplace operator.

Affiliated with

Also associated with

No associations

Rating

On the geometry of Kähler-Poisson structures 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 On the geometry of Kähler-Poisson structures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the geometry of Kähler-Poisson structures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-567664