Artículos de revistas
Interpolation of geometric structures compatible with a pseudo Riemannian metric
Fernández Culma, Edison Alberto; Godoy, Yamile Alejandra; Salvai, Marcos Luis; Interpolation of geometric structures compatible with a pseudo Riemannian metric; Springer; Manuscripta Mathematica; 151; 3-4; 11-2016; 453-468
Fernández Culma, Edison Alberto
Godoy, Yamile Alejandra
Salvai, Marcos Luis
Let (M, g) be a pseudo Riemannian manifold. We consider four geometric structures on M compatible with g: two almost complex and two almost product structures satisfying additionally certain integrability conditions. For instance, if r is paracomplex and symmetric with respect to g, then r induces a pseudo Riemannian product structure on M. Sometimes the integrability condition is expressed by the closedness of an associated two-form: if j is almost complex on M and ω(x, y) = g(jx, y) is symplectic, then M is almost pseudo Kähler. Now, product, complex and symplectic structures on M are trivial examples of generalized (para)complex structures in the sense of Hitchin. We use the latter in order to define the notion of interpolation of geometric structures compatible with g. We also compute the typical fibers of the twistor bundles of the new structures and give examples for M a Lie group with a left invariant metric.