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Generalized geometry of pseudo-Riemannian manifolds and the generalized ∂̅-operator
Veröffentlicht/Copyright:
16. April 2016
Abstract
Let (M, g, ∇) be a pseudo-Riemannian manifold with a torsion free linear connection and let Jg be the generalized complex structure on M defined by g; see [13], [14]. We prove that in the case Jg is ∇- integrable the ±i-eigenbundles of Jg, E1,0Jg and E0,1Jg are complex Lie algebroids.Moreover E0,1Jg and (E1,0Jg)* are canonically isomorphic, thus we define the concept of generalized ∂̅-operator of (M, g, ∇) and we describe a class of generalized holomorphic sections of T(M) ⊕ T*(M). Also we relate the Lie bialgebroid property of (E1,0Jg , (E1,0Jg )*) to conditions on the metric g in the case of affine Hessian manifolds.
Keywords: General geometric structures on manifolds; Hessian manifolds; generalized geometry; Lie algebroids; Lie bialgebroids
Received: 2014-4-3
Revised: 2014-10-7
Published Online: 2016-4-16
Published in Print: 2016-4-1
© 2016 by Walter de Gruyter Berlin/Boston
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Artikel in diesem Heft
- Frontmatter
- Cycles in Jacobians: infinitesimal results
- Totally isotropic subspaces of small height in quadratic spaces
- Generalized geometry of pseudo-Riemannian manifolds and the generalized ∂̅-operator
- Homogeneous geodesics in pseudo-Riemannian nilmanifolds
- Generalized distance-squared mappings of the plane into the plane
- Stable hypersurfaces in spheres with constant scalar curvature
- On the axioms for Sabinin algebras
-
Extremal effective divisors of Brill–Noether and Gieseker–Petri type in
- On spherical submanifolds with finite type spherical Gauss map
- The second largest Erdős–Ko–Rado sets of generators of the hyperbolic quadrics Q+(4n + 1, q)
Schlagwörter für diesen Artikel
General geometric structures on manifolds;
Hessian manifolds;
generalized geometry;
Lie algebroids;
Lie bialgebroids
Artikel in diesem Heft
- Frontmatter
- Cycles in Jacobians: infinitesimal results
- Totally isotropic subspaces of small height in quadratic spaces
- Generalized geometry of pseudo-Riemannian manifolds and the generalized ∂̅-operator
- Homogeneous geodesics in pseudo-Riemannian nilmanifolds
- Generalized distance-squared mappings of the plane into the plane
- Stable hypersurfaces in spheres with constant scalar curvature
- On the axioms for Sabinin algebras
-
Extremal effective divisors of Brill–Noether and Gieseker–Petri type in
- On spherical submanifolds with finite type spherical Gauss map
- The second largest Erdős–Ko–Rado sets of generators of the hyperbolic quadrics Q+(4n + 1, q)
