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- W4300501669 abstract "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-Weitzenbock 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." @default.
- W4300501669 created "2022-10-03" @default.
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- W4300501669 date "2015-04-23" @default.
- W4300501669 modified "2023-10-18" @default.
- W4300501669 title "Bochner's technique for statistical structures" @default.
- W4300501669 doi "https://doi.org/10.48550/arxiv.1504.06307" @default.
- W4300501669 hasPublicationYear "2015" @default.
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