AN ABSTRACT MORIMOTO THEOREM FOR GENERALIZED<i>F</i>-STRUCTURES

Aldi, Marco; Grandini, Daniele

doi:10.1093/qmath/haw004

Cited by 5 publications

(3 citation statements)

References 19 publications

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“…The vanishing of the right hand side becomes the second condition which holds for any vector fields on a Hermitian manifold, and, in the end, replace Y by JY . (Identity (3.12) may be checked on any combination of arguments of the complex type (1, 0), (0, 1) while recalling that dΩ has only terms of type (2, 1), (1,2). )…”

Section: Induced Structures Of Hypersurfacesmentioning

confidence: 99%

“…The (2, 1)-generalized almost contact structures were also introduced under a different form in [13], where the author looks at E ± = (1/2)(Z + ± Z − ) rather than at Z ± . Notice that, if (F , Z ± ) is a (2, 1)-generalized almost contact structure, L = im F is a split structure in the sense of [1,2].…”

Section: (2 1)-generalized Almost Contact Structuresmentioning

confidence: 99%

“…An almost contact structure of M is normal iff the corresponding almost complex structure of M × R is integrable and the normality condition is 1 (2.6)…”

Section: Preliminariesmentioning

confidence: 99%

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On hypersurfaces of generalized Kähler manifolds

Vaisman

2018

Differential Geometry and its Applications

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ABSTRACT. We establish the conditions for the induced generalized metric F structure of an oriented hypersurface of a generalized Kähler manifold to be a generalized CRFK structure. Then, we discuss a notion of generalized almost contact structure on a manifold M that is suggested by the induced structure of a hypersurface. Such a structure has an associated generalized almost complex structure on M ×R. If the latter is integrable, the former is normal and we give the corresponding characterization. If the structure on M × R is generalized Kähler, the structure on M is said to be binormal. We characterize binormality and give an example of binormal structure.

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Section: Induced Structures Of Hypersurfacesmentioning

confidence: 99%

Section: (2 1)-generalized Almost Contact Structuresmentioning

confidence: 99%

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On hypersurfaces of generalized Kähler manifolds

Vaisman

2018

Differential Geometry and its Applications

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Quasi-classical generalized CRF structures

Vaisman

2016

Ann Glob Anal Geom

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ABSTRACT. In an earlier paper, we studied manifolds M endowed with a generalized F structure Φ ∈ End(T M ⊕ T * M ), skew-symmetric with respect to the pairing metric, such that Φ 3 + Φ = 0. Furthermore, if Φ is integrable (in some well-defined sense), Φ is a generalized CRF structure. In the present paper we study quasi-classical generalized F and CRF structures, which may be seen as a generalization of the holomorphic Poisson structures (it is well known that the latter may also be defined via generalized geometry). The structures that we study are equivalent to a pair of tensor fields (A ∈ End(T M ), π ∈ ∧ 2 T M ) where A 3 + A = 0 and some relations between A and π hold. We establish the integrability conditions in terms of (A, π). They include the facts that A is a classical CRF structure, π is a Poisson bivector field and im A is a (non)holonomic Poisson submanifold of (M, π). We discuss the case where either ker A or im A is tangent to a foliation and, in particular, the case of almost contact manifolds. Finally, we show that the dual bundle of im A inherits a Lie algebroid structure and we briefly discuss the Poisson cohomology of π, including an associated spectral sequence and a Dolbeault type grading.

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Polynomial structures in generalized geometry

Aldi

Grandini

2022

Differential Geometry and its Applications

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AN ABSTRACT MORIMOTO THEOREM FOR GENERALIZEDF-STRUCTURES

Cited by 5 publications

References 19 publications

On hypersurfaces of generalized Kähler manifolds

On hypersurfaces of generalized Kähler manifolds

Quasi-classical generalized CRF structures

Polynomial structures in generalized geometry

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