Surface theory in four-dimensional Galilean space
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This paper develops several fundamental aspects of the theory of surfaces in four-
dimensional Galilean space. The first and second fundamental forms of a surface are introduced and
used to define the normal curvature, principal curvatures, mean curvatures, and total curvature.
The principal curvatures are characterized as extremal values of the normal curvature. Derivative
formulas for surfaces are established, leading to relations that express the coefficients of the second
fundamental form in terms of the coefficients of the first fundamental form and their partial
derivatives. As a consequence, the mean and total curvatures are represented without explicit use of
the coefficients of the second fundamental form.
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