On a Class of Almost-Hermitian Structures on Tangent Bundles

摘要

We construct a new almost-Hermitian structure of anti-invariant type on tangent bundles and deduce criteria for this structure to belong to all the Gray-Hervella classes. In particular, we prove that the tangent bundles over Kahlerian and semi-Kahlerian manifolds carry, respectively, a Kahlerian and a semi-Kahlerian structure.