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Abstract:
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This work provides the surface shape analysis in R3 using the
shape operator, i.e. using the curvatures as well as curvature's
functionals such as the Willmore energy. Then, there were
considered changes of surfaces' geometric characteristics
under infinitesimal deformations, and specialy, curvature based
functionals variations under infinitesimal bending of surface.
Special kinds of ruled surfaces were analysed from geometrical
and constructional point of view, and pointed to their wide use.
At last, there is a generalization by considering the Finsler and
the generalized Finsler spaces. |