Bochner’s technique for statistical structures

By B. Opozda. 2015

78 citations recorded by the source corpus.

The main aim of this paper is to extend Bochner’s technique to statistical structures. Other topics related to this technique are also introduced to the theory of statistical structures. It deals, in particular, with Hodge’s theory, Bochner–Weitzenböck and Simon’s type formulas. Moreover, a few global and local theorems on the geometry of statistical structures are proved, for instance, theorems saying that under some topological and geometrical conditions a statistical structure must be trivial. We also introduce a new concept of sectional curvature depending on statistical connections. On the base of this notion we study the curvature operator and prove some analogues of well-known theorems from Riemannian geometry.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/acfcf2731077197077c3a546ae518d1ea37e54a6

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1. B. Opozda

Citations in the corpus

• A sectional curvature for statistical structures (2015, background): “This idea is discussed in [8] for statistical structures on abstract manifolds, that is, on manifolds (not necessarily immersed in any standard space) endowed with a matric tensor field g and a torsion-free affine connection ∇ for which ∇g as a 3-covariant tensor is symmetric.”