Infinitesimal bendings for classes of two-dimensional surfaces

Global hypoellipticity for strongly invariant operators

“…As |B| 2 = 0, we can conclude that σ L (ξ ℓ ) − A = 0 and σ L (−ξ ℓ ) − Ā = 0 for all ℓ ∈ N. In this context, (6) implies the existence of infinitely many compatibility conditions for the Fourier coefficients of f ∈ C ∞ (T n ) to satisfy P u = f . Consequently, P is not solvable according to our definition.…”

“…In the broader context of compact Lie groups, some initial results are presented in [7,9,10]. Additional references regarding infinitesimal deformations of surfaces connected with solvability of Vekua-type operators include [6,12,13] and references therein…”

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.…”