We propose a class of N = 2 supersymmetric nonlinear sigma models on the noncompact Ricci-flat Kähler manifolds, interpreted as the complex line bundles over the hermitian symmetric spaces. Kähler potentials and Ricci-flat metrics for these manifolds with isometries are explicitly constructed by using the techniques of supersymmetric gauge theories. Each of the metrics contains a resolution par...

A method, due tó Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is s...

where (hαβ) is the positive definite n × n matrix on M , which is uniquely determined by the Levi form Lθ(u, v) = −idθ(u, v) for u, v ∈ H(M). Let ∆sb be the sub-Laplacian with respect to θ (see [8], [22] and [7] for references) and let μ1 be the first positive eigenvalue of ∆sb on (M, θ). Let Rαβ be the Webster pseudo Ricci curvature, R be the pseudo scalar curvature and Tor be the pseudo torsi...