Hodge decomposition theorem on strongly Kaehler Finsler manifolds

摘要

Faran posed an open problem about analysis on complex Finsler spaces: Is there an analogue of the partial deriv-Laplacian? Is there an analogue of Hodge theory? Under the assumption that (M, F) is a compact strongly Kaehler Finsler manifold, we define a partial deriv-Laplacian on the base manifold. Our result shows that the well-known Hodge decomposition theorem in Kaehler manifolds is still true in the more general compact strongly Kaehler Finsler manifolds.