Abstract

A family {*Sτ*} of surfaces *Sτ* with the unit normal *τ = τ (x, y, z)* in
the Euclidean space *E3* is considered. The surfaces *Sτ* continuously fill a domain *D*
in *E3*. For the family {*Sτ*} of surfaces *Sτ*, the law of conservation div ** F** = 0
is proved, where the solenoidal vector field

**is expressed in terms of the main classical characteristics of the surfaces**

*F**Sτ*: the unit normal, the principal directions, the principal curvatures, the mean curvature, and the Gaussian curvature.

Keywords

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megrabov3.pdf224.09 KB

Pages

51-58