classical differential geometryClassicalDifferentialGeometry2005-05-18 14:00:112009-04-04 06:57:15Topic% this is the default PlanetMath preamble. as your knowledge
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\newtheorem{cor}{Corollary}\subsection*{Curves in $\R^2$}
\begin{itemize}
\item inflexion point
\item singular points of plane curve
\item isocline
\item curvature (plane curve)
\item circle of curvature
\item curvature determines the curve
\item curvature of Nielsen's spiral
\item osculating curve
\item orthogonal curves
\item parallel curves
\item properties of parallel curves
\item evolute
\item evolute of cycloid
\item \PMlinkname{Serret-Frenet equations in $\R^2$}{SerretFrenetEquationsInMathbbR2}
\item Famous curves in the plane
\item arc-parametrizations
\item envelope
\item determining envelope
\item catacaustic
\end{itemize}
\subsection*{Curves in $\R^3$}
\begin{itemize}
\item \PMlinkname{Serret-Frenet equations in $\R^3$}{SerretFrenetFormulas}
\item space curve
\item level curve
\item \PMlinkname{curvature}{CurvatureOfACurve} and \PMlinkname{torsion}{Torsion} of a space curve
\item moving trihedron
\end{itemize}
\subsection*{Surfaces in $\R^3$}
\begin{itemize}
\item level curve, level surface
\item surface of revolution
\item surface normal
\item normal section
\item normal curvatures
\item Meusnier's theorem
\item mean curvature at surface point
\item \PMlinkname{first fundamental form}{FirstFundamentalForm}
\item second fundamental form
\item sphere map and shape operator
\item Gaussian curvature and mean curvature
\item geodesic
\item variational calculus
\item Gauss-Bonnet theorem
\item standard connection in $\R^3$
\item Gauss equation
\end{itemize}
\subsection*{The space $\R^3$}
\begin{itemize}
\item ortho-normal frame fields in $\R^3$ (or non constant ortho-normal triples of vector fields)
\item rate of rotation of an o.f.f.
\item euclidean spin connection
\item $\R^3$ {\bf Cartan structural equations I,II}
\end{itemize}