Transformations and coupling relations for affine connections

DOI10.1016/j.difgeo.2016.06.006zbMath1353.53016OpenAlexW2505615175WikidataQ115355660 ScholiaQ115355660MaRDI QIDQ344160

James Tao, Jun Zhang

Publication date: 22 November 2016

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2016.06.006

zbMATH Keywords

torsioninformation geometryCodazzi couplingCodazzi transformationconformal-projective transformationconjugate connection

Mathematics Subject Classification ID

Statistical aspects of information-theoretic topics (62B10) Connections (general theory) (53C05) Local Riemannian geometry (53B20) Linear and affine connections (53B05) Other connections (53B15)

Related Items (7)

Interaction of Codazzi couplings with (para-)Kähler geometry ⋮ Statistical mirror symmetry ⋮ Complex affine distributions ⋮ (Para-)holomorphic and conjugate connections on (para-)Hermitian and (para-)Kähler manifolds ⋮ Almost product structures on statistical manifolds and para-Kähler-like statistical submersions ⋮ 1-conformal geometry of quasi statistical manifolds ⋮ From Hessian to Weitzenböck: manifolds with torsion-carrying connections

Cites Work

• On realization of conformally-projectively flat statistical manifolds and the divergences
• Higher order Codazzi tensors on conformally flat spaces
• Geometric methods for solving Codazzi and Monge-Ampère equations
• On the divergence of 1-conformally flat statistical manifolds
• Codazzi tensors and the topology of surfaces
• On \(\alpha\)-conformal equivalence of statistical submanifolds
• On dual-projectively flat affine connections
• Transformation techniques for partial differential equations on projectively flat manifolds
• Codazzi-equivalent affine connections
• Geometry of Pre-contrast Functions and Non-conservative Estimating Functions
• Conformal-Projective Geometry of Statistical Manifolds
• Divergence Function, Duality, and Convex Analysis
• KV Cohomology in Information Geometry
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