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A note on the Gauss–Bonnet–Chern theorem for general connection

Journal of Geometry and Physics, 2015
In this paper, we prove a local index theorem for the DeRham Hodge-laplacian which is defined by the connection compatible with metric. This connection need not be the Levi-Civita connection. When the connection is Levi-Civita connection, this is the classical local Gauss-Bonnet-Chern theorem.
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A characterization of the Chern and Bernwald connections

1996
Let \(M\) be a smooth manifold and \(\pi:TM\to M\) its tangent bundle. The vertical subbundle \(V\subset T(TM)\) is \(\text{Ker} D\pi\) and a supplement of it is a horizontal bundle. A linear connection in \(V\) is good if it can be canonically prolonged to \(TM\).
openaire   +2 more sources

Shen's L-process on the Chern connection

2023
Faghfouri, Morteza, Jazer, Nadereh
openaire   +2 more sources

On the linearization stability of the Chern-scalar curvature

Mathematische Zeitschrift, 2022
Francesco Pediconi, Daniele Angella
exaly  

Curvature of Chern connections

2017
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Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances

Journal of the Physical Society of Japan, 2005
Yasuhiro Hatsugai, Takahiro Fukui, Suzuki Hiroshi   +2 more
exaly  

Remarks on Chern–Einstein Hermitian metrics

Mathematische Zeitschrift, 2019
Cristiano Spotti, Daniele Angella
exaly  

Berry Phase, Berry Connection, and Chern Number for a Continuum Bianisotropic Material From a Classical Electromagnetics Perspective

IEEE Journal on Multiscale and Multiphysics Computational Techniques, 2017
George Hanson, Mario Silveirinha, S Ali Hassani Gangaraj   +2 more
exaly  

Chern-flat and Ricci-flat invariant almost Hermitian structures

Annals of Global Analysis and Geometry, 2010
Luigi Vezzoni, Antonio J di Scala, Di Scala Antonio J   +2 more
exaly