Tensor product surfaces of a Euclidean space curve and a Euclidean plane curve.
We prove the vanishing of the kernel of the Dolbeault operator of the square root of the canonical line bundle of a compact Hermitian spin surface with positive scalar curvature. We give lower estimates of the eigenvalues of this operator when the conformal scalar curvature is non -negative.
It is shown that one can define a Hilbert space structure over a kaehlerian manifold with global potential in a natural way.