Paraholomorphic B-manifold and its properties

“…In order to unify the property that says when an F -symmetric r -form is almost F -analytic for both almost complex and paracomplex cases, we present: [18]: [5,6,7,10,12,15,18], the tensor field ω is called almost F -analytic if Φ F ω = 0 and for r -forms this condition is equivalent to (2.26).…”

Section: Ii) More Generally Than I) If ε = +1 Then a F -Hybrid 2 -Formentioning

confidence: 99%

Almost analytic forms with respect to a quadratic endomorphism and their cohomology

Crâşmăreanu

Ida

2015

Turk J Math

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The goal of this paper is to consider the notion of almost analytic form in a unifying setting for both almost complex and almost paracomplex geometries. We use a global formalism, which yields, in addition to generalizations of the main results of the previously known almost complex case, a relationship with the Frölicher-Nijenhuis theory. A cohomology of almost analytic forms is also introduced and studied as well as deformations of almost analytic forms with pairs of almost analytic functions.

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“…We note that Φ ϕ ω ∈ 0 q+1 (M 2n ). If Φ ϕ ω = 0, then ω is said to be almost paraholomorphic with respect to the paracomplex algebra R (j) ,( [6], [11]). …”

Section: Para-nordenian Properties Of S Gmentioning

confidence: 99%