Riv. Mat. Univ. Parma, Vol. 13, No. 2, 2022
Adara M. Blaga ^{[a]} and Antonella Nannicini ^{[b]}
Statistical structures, αconnections and Generalized Geometry
Pages: 283296
Received: 22 September 2021
Accepted: 24 May 2022
Mathematics Subject Classification: 53C15, 53C05, 53C38.
Keywords: Statistical structures, αconnections, generalized geometry.
Authors address:
[a]: West University of Timisoara, Department of Mathematics, Timisoara, Romania
[b]: University of Florence, Dipartimento di Matematica e Informatica “U. Dini”, Florence, Italy
This research was partially supported by the PRIN 2017 project ''Real and Complex
Manifolds: Topology, Geometry and holomorphic dynamics'' (code 2017JZ2SW5)
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Abstract:
The main purpose of this paper is to describe how statistical structures fit perfectly into Generalized Geometry.
Firstly, we will briefly present the properties of generalized pseudocalibrated almost complex structures induced
by statistical structures. Then we will characterize the integrability of generalized almost complex structures
with respect to the bracket defined by the \(\alpha\)connection, finding conditions under which the concept of
integrability is \(\alpha\)invariant. Finally, we consider a pair of generalized dual quasistatistical
connections \((\hat{\nabla},\hat{\nabla}^*)\) on the generalized tangent bundle \(TM\oplus T^*M\) and we provide
conditions for \(TM\oplus T^*M\) with the \(\alpha\)connections \((\hat{\nabla}^{(\alpha)},\hat{\nabla}^{(\alpha)})\)
induced by \((\hat{\nabla},\hat{\nabla}^*)\) to be conjugate Riccisymmetric.
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