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This paper concerns the existence and explicit construction of extremal Kähler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach,… (More)

We write an ansatz for quasi-Einstein Kähler metrics and construct new complete examples. Moreover, we construct new compact generalized quasi-Einstein Kähler metrics on some ruled surfaces,… (More)

This paper produces explicit strongly Hermitian Einstein–Maxwell solutions on the smooth compact 4-manifolds that are $$S^2$$S2-bundles over compact Riemann surfaces of any genus. This generalizes… (More)

We provide nontrivial examples of solutions to the system of coupled equations introduced by M. García-Fernández for the uniformization problem of a triple (M; L; E), where E is a holomorphic vector… (More)

It is shown that if a minimal ruled surface admits a K\"ahler Yamabe minimizer, then this metric must be generalized K\"ahler-Einstein and the underlying holomorphic vector bundle of the ruled… (More)

We prove the existence of extremal Sasakian structures occurring on a countably infinite number of distinct contact structures on T ×S and certain related 5-manifolds. These structures occur in… (More)

We prove the existence of extremal Sasakian structures occurring on a countably infinite number of distinct contact structures on $T^2\times S^3$ and certain cyclic quotients. These structures occur… (More)