The ciconia metric on the tangent bundle of an almost-Hermitian manifold

Abstract

We find a new class of invariant metrics existing on the tangent bundle of any given almost-Hermitian manifold. We focus here on the case of Riemannian surfaces, which yield new examples of Kählerian Ricci-flat manifolds in four real dimensions.

Some improvements; this version has one more page with proofs and a picture of a "ciconia" from Alentejo, Portugal. Published online in Annali di Matematica Pura ed Applicata (2019)

References in corpus (2)

• Homotheties and topology of tangent sphere bundles
• On vector bundle manifolds with spherically symmetric metrics

Cited by in corpus (1)

• Notes on the Sasaki metric