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\begin{document}
\section{Fermat's Principle}
Initially conceived in optics, \emph{Fermat's principle} was stated as the principle of least time for traveling light \htmladdnormallink{waves}{http://planetphysics.us/encyclopedia/CosmologicalConstant2.html}, that is the path or paths taken between two points by light which can be traversed in the least time; in an Euclidean space or a flat Minkowski space, this is the straight line defined by a single ray of light. This can be thought as the trajectory of an emitted photon traveling at the universal maximum \htmladdnormallink{speed}{http://planetphysics.us/encyclopedia/Velocity.html} $c$ in vacuum. In a Riemannian
or Minkowski \htmladdnormallink{spacetime}{http://planetphysics.us/encyclopedia/SR.html} this corresponds to the surface of a light cone.
In general relativity, however, a \htmladdnormallink{point particle}{http://planetphysics.us/encyclopedia/CenterOfGravity.html} path is a \htmladdnormallink{geodesic}{http://planetphysics.us/encyclopedia/GeodesicEquation.html} curve in a Riemannian space that can be curved, for example, by the presence of intense gravitational \htmladdnormallink{fields}{http://planetphysics.us/encyclopedia/CosmologicalConstant2.html}. One such effect was observed and reported by modern astrophysicists and is called \emph{gravitational lensing}.
\subsubsection{Minimum Action Principles in Electromagnetism and Quantum Theories}
\end{document}
