$\kappa$urvature

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Curvature For Galaxy Structural Analysis

November 2019
NOTE: Page under development. Now, I am testing some $\LaTeX$ typesetting in HTML (not figures of equations...).

1 | A little about curvature

1.1 | Introduction

The curvature is introduced as a new non-parametric tool for galaxy structural analysis....


1.2 | What is curvature in differential geometry?

From differential geometry we have $$ \widetilde{\kappa}(R) = \frac{d^2 I}{d R^2} \left[ 1+ \left( \frac{d I}{dR} \right)^2 \right]^{-3/2} $$

The Riemann curvature tensor is \begin{align} R^{\kappa}_{\lambda \mu \nu} = \Gamma^{\kappa}_{\lambda \nu, \mu} - \Gamma^{\kappa}_{\lambda \mu, \nu} + \Gamma^{\kappa}_{\rho \mu}\Gamma^{\rho}_{\lambda \nu} - \Gamma^{\kappa}_{\rho \nu} \Gamma^{\rho}_{\lambda \mu} \end{align}

More tests....

\begin{align} \phi_n = \frac{2n\pi}{1-\dfrac{3GM}{c^2 a_0(1-e^2)}}, \quad n=0,1,2... \end{align}

\begin{align} g_{\mu \nu } = {\rm diag} \left[ -\left(1 - \frac{2GM}{rc^2} \right) , \left(1 - \frac{2GM}{rc^2} \right)^{-1},r^2, r^2 \sin^2 \theta\right] \end{align}


2 | $\kappa$urvature in Medical Sciences


2 | How $\kappa$urvature can be used in galaxy morphology


3 | Annimations & Cartoons

Bellow... (testing some videos)

Curvature for NGC1211 from EFIGI.

Curvature for NGC4267 from EFIGI.