A paracomplex structure on a manifold M is an endomorphism K of the tangent bundle TM such that K(2) = I, whose +/- 1-eigenspaces have the same dimension and are involutive. By using the theory of differential graded Lie algebras, we describe small deformations of paracomplex structures. We also compute the space of invariant small deformations of 4-dimensional nilmanifolds endowed with a fixed paracomplex structure. By using the theory of differential graded Lie algebras, we describe small deformations of paracomplex structures. We also compute the space of invariant small deformations of 4-dimensional nilmanifolds endowed with a fixed paracomplex structure.
On small deformations of paracomplex manifolds / Medori, Costantino; Tomassini, Adriano. - In: JOURNAL OF NONCOMMUTATIVE GEOMETRY. - ISSN 1661-6952. - 5:4(2011), pp. 507-522. [10.4171/JNCG/84]
On small deformations of paracomplex manifolds
MEDORI, Costantino;TOMASSINI, Adriano
2011-01-01
Abstract
A paracomplex structure on a manifold M is an endomorphism K of the tangent bundle TM such that K(2) = I, whose +/- 1-eigenspaces have the same dimension and are involutive. By using the theory of differential graded Lie algebras, we describe small deformations of paracomplex structures. We also compute the space of invariant small deformations of 4-dimensional nilmanifolds endowed with a fixed paracomplex structure. By using the theory of differential graded Lie algebras, we describe small deformations of paracomplex structures. We also compute the space of invariant small deformations of 4-dimensional nilmanifolds endowed with a fixed paracomplex structure.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
