Einstein--Finsler vector bundles
Copyright policy )Einstein--Finsler vector bundles
First, an invariant definition of the Einstein-Finsler condition is given in terms of the curvature tensor of a partial connection in a holomorphic vector bundle with a complex Finsler structure. Then a Bochner-type vanishing theorem for holomorphic sections is shown. The last section deals with the semi-stability of Einstein-Finsler bundles. It is proved that if an Einstein-Finsler bundle over a compact Kähler manifold is either modeled on a complex Minkowski space or is partially reducible, then it is \(\Phi\)-semi-stable.
partial connections, Special Riemannian manifolds (Einstein, Sasakian, etc.), Einstein-Finsler structures, Local differential geometry of Finsler spaces and generalizations (areal metrics), semistability, complex Finsler structures
partial connections, Special Riemannian manifolds (Einstein, Sasakian, etc.), Einstein-Finsler structures, Local differential geometry of Finsler spaces and generalizations (areal metrics), semistability, complex Finsler structures
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