  In 2010, a book published on the work of Jaques Hadamard, entitled
"Introduction to Tensor Analysis and the Calculus of Moving Surfaces" by Dr.
Pavel Grinfeld, proposed an extension of Hadamard's work to ultimately allow
principles of tensorial invariance on surfaces to be extended to notions of
time-dependent and moving surfaces. Coined "The Calculus of Moving Surfaces"
(CMS), notions of Invariant Time Derivatives on Arbitrary Surface/Ambient
Tensors, Surface Velocities, and time derivatives of time-dependent Volume &
Surface Integrals were introduced. This paper focuses on extending concepts
found within CMS to other Surface Objects, to Higher Orders, and to further
uncover Tensors which are powerful at representing Commutations and Curvature
present on Surfaces which are moving in Time.
