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

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.

Affine Connections

2013 ◽  
pp. 631-664
Author(s):  
Norbert Straumann
Keyword(s):  
Affine Connections

Affine connections

1934 ◽  
pp. 13-23
Author(s):  
D. J. Struik
Keyword(s):  
Affine Connections

scholarly journals ON THE EXISTENCE OF AFFINE CONNECTIONS WITH RECURRENT PROJECTIVE CURVATURE

2000 ◽  
Vol 33 (1) ◽  
Author(s):  
Zbigniew Olszak ◽  
Karina Słuka
Keyword(s):  
Affine Connections ◽  
Projective Curvature

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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