On Two Affine Connections

1989 ◽  
pp. 40-51
Author(s):  
Shiing-Shen Chern
Keyword(s):  
Affine Connections

scholarly journals Color algebras and affine connections on S6

1992 ◽  
Vol 149 (1) ◽  
pp. 234-261 ◽  
Author(s):  
Alberto Elduque ◽  
Hyo Chul Myung
Keyword(s):  
Affine Connections

scholarly journals Hooke’s law in statistical manifolds and divergences

2000 ◽  
Vol 159 ◽  
pp. 1-24 ◽  
Author(s):  
Masayuki Henmi ◽  
Ryoichi Kobayashi
Keyword(s):  
Classical Mechanics ◽  
Riemannian Metric ◽  
Legendre Transform ◽  
Point Function ◽  
Hooke’S Law ◽  
Affine Connections ◽  
Statistical Manifolds ◽  
Dual Affine ◽  
Hooke's Law

The concept of the canonical divergence is defined for dually flat statistical manifolds in terms of the Legendre transform between dual affine coordinates. In this article, we introduce a new two point function defined for any triple (g,∇, ∇*) of a Riemannian metric g and two affine connections ∇ and ∇*. We show that this interprets the canonical divergence without refering to the existence of special coordinates (dual affine coordinates) but in terms of only classical mechanics concerning ∇- and ∇*-geodesics. We also discuss the properties of the two point function and show that this shares some important properties with the canonical divergence defined on dually flat statistical manifolds.

On Affine Connections Induced on the (1, 1)-Tensor Bundle

2018 ◽  
Vol 39 (4) ◽  
pp. 683-694
Author(s):  
Murat Altunbas ◽  
Aydin Gezer
Keyword(s):  
Affine Connections ◽  
Tensor Bundle

Affine connections on 3-Sasakian and manifolds

2019 ◽  
Vol 294 (1-2) ◽  
pp. 817-868 ◽  
Author(s):  
Cristina Draper ◽  
Miguel Ortega ◽  
Francisco J. Palomo
Keyword(s):  
Affine Connections
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