The Structure Equations of a Complex Finsler Manifold

Details The Structure Equations of a Complex Finsler Manifold The Structure Equations of a Complex Finsler Manifold

1999-10-07

arxiv.org/abs/math/9910040v1

Mathematics

Differential Geometry

Scientific paper

For a strongly pseudo-convex complex Finsler manifold M, a bundle U of adapted unitary frames is canonically defined. A non-linear Hermitian connection on U, invariant under local biholomorphic isometries, is given and it proved to be unique. By means of such connection, an absolute parallelism on U is determined and a new set of structure functions which generate all the isometric invariants of a Finsler metric is obtained. A pseudo-convex complex Finsler manifolds M, which admits a totally geodesic complex curve with a given constant holomorphic sectional curvature through any point and any direction, is called E-manifold. Main examples of E-manifolds are the smoothly bounded, strictly convex domains in C^n, endowed with the Kobayashi metric. A complete characterization of E-manifolds, using the previously defined structure functions, is given and a smaller set of generating functions for the isometric invariants of E-manifolds is determined.

Affiliated with

Also associated with

No associations

Rating

The Structure Equations of a Complex Finsler Manifold 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 The Structure Equations of a Complex Finsler Manifold, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Structure Equations of a Complex Finsler Manifold will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-661809