Interpolation of geometric structures compatible with a pseudo Riemannian metric

 

Autores
Fernández Culma, Edison Alberto; Godoy, Yamile Alejandra; Salvai, Marcos Luis
Tipo de recurso
artículo
Estado
Versión publicada
Año de publicación
2016
País
Argentina
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio
CONICET Digital (CONICET)
Descripción
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.
Idioma
inglés
OAI Identifier
oai:ri.conicet.gov.ar:11336/58454
Enlace del recurso
http://hdl.handle.net/11336/58454
Nivel de acceso
Acceso abierto
Materia
22F30
22F50
53B30
53B35
53C15
53C56
53D05
Matemática Pura
Matemáticas
CIENCIAS NATURALES Y EXACTAS