caa a22 4500 60549651X CHVBK 20210128100536.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10231-014-0431-5 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0431-5 Salvai Marcos FaMAF-CIEM, Ciudad Universitaria, Medina Allende s/n, 5000, Córdoba, Argentina aut Generalized geometric structures on complex and symplectic manifolds [Elektronische Daten] [Marcos Salvai] On a smooth manifold $$M$$ M , generalized complex (generalized paracomplex) structures provide a notion of interpolation between complex (paracomplex) and symplectic structures on $$M$$ M . Given a complex manifold $$\left( M,j\right) $$ M , j , we define six families of distinguished generalized complex or paracomplex structures on $$M$$ M . Each one of them interpolates between two geometric structures on $$M$$ M compatible with $$j$$ j , for instance, between totally real foliations and Kähler structures, or between hypercomplex and $$\mathbb {C}$$ C -symplectic structures. These structures on $$M$$ M are sections of fiber bundles over $$M$$ M with typical fiber $$G/H$$ G / H for some Lie groups $$G$$ G and $$H$$ H . We determine $$G$$ G and $$H$$ H in each case. We proceed similarly for symplectic manifolds. We define six families of generalized structures on $$\left( M,\omega \right) $$ M , ω , each of them interpolating between two structures compatible with $$\omega $$ ω , for instance, between a $$\mathbb {C}$$ C -symplectic and a para-Kähler structure (aka bi-Lagrangian foliation). Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Generalized complex structure nationallicence Interpolation nationallicence Kähler nationallicence Hypercomplex nationallicence Signature nationallicence Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/5(2015-10-01), 1505-1525 0373-3114 194:5<1505 2015 194 10231 https://doi.org/10.1007/s10231-014-0431-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0431-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Salvai Marcos FaMAF-CIEM, Ciudad Universitaria, Medina Allende s/n, 5000, Córdoba, Argentina aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/5(2015-10-01), 1505-1525 0373-3114 194:5<1505 2015 194 10231