An Analytical Inflexibility of Surfaces Attached Along a Curve to a Surface Regarding a Point and Plane

Characterization of dual curves using the theory of infinitesimal bending

“…The problems of infinitesimal bending of curves and surfaces in Euclidean 3‐space are an important part of differential geometry and are discussed in [8–19, 21–24] and so forth. Based on these considerations, primarily on papers [11, 17, 22, 24], we will generalize the basic concepts and statements to dual 3‐space .…”

“…Infinitesimal bending theory has numerous applications in mathematics and mechanics, especially in the theory of thin shells. Some recent papers on this topic are [8–17]…”

“…Infinitesimal bending theory has numerous applications in mathematics and mechanics, especially in the theory of thin shells. Some recent papers on this topic are [8][9][10][11][12][13][14][15][16][17] It is interesting to study the influence of infinitesimal bending on ruled surfaces and their flexibility. As is well known, a surface is said to be ruled if at every point of the surface there is a straight line lying on the surface.…”

Improving waste recycling in Uzbekistan in digital technologies

“…The creation of a whole system of scientific, production and trade will be based on objective laws, as well as determined by scientific and technological progress and the market needs of the enterprise [21].…”

Curves on ruled surfaces under infinitesimal bending

“…Many other geometric magnitudes stay invariant in the sense that they don't get the variations of the first order (for example, the coefficients of the first fundamental form, Cristoffel's symbols, Gaussian curvature etc.). Many papers are devoted to the infinitesimal bending of curves, surfaces and manifolds (see (Aleksandrov, 1936;Efimov, 1948;Kon-Fossen, 1959;Vekua, 1959;Ivanova-Karatopraklieva & Sabitov, 1995;Velimirović, 2001a,b;Hinterleitner et al, 2008;Rančić et al, 2009;Alexandrov, 2010;Najdanović, 2015;Najdanović & Velimirović, 2017;Kauffman et al, 2019;Najdanović et al, 2019;Rančić et al, 2019;Rýparová & Mikeš, 2019;Belova et al, 2021;Maksimović et al, 2021).…”