The mathematics of DNA molecules is often studied as a double helix model. This paper focuses on the modelling of infinitesimal bending of DNA helices. The paper checks the flexibility of DNA molecule, i.e. the flexibility of double helix in infinitesimal bending theory. Actually, first, we find infinitesimal bending field of an arbitrary curve on the helicoid, that leaves bent curves on the helicoid, and show that helix bending on the helicoid is not possible.Finally, we deal with the infinitesimal bending of helicoid, using PDEs. Visualization of infinitesimal bending was done in Mathematica.
Infinitesimal bending of curves lying with a given precision on ruled surfaces in 3-dimensional Euclidean space is studied. In particular, the bending of curves on the cylinder, the hyperbolic paraboloid and the helicoid are considered and appropriate bending fields are found. Some examples are graphically presented.
The purpose of this paper is to investigate the product semi-symmetric connection in a locally decomposable Riemannian space. The curvature tensors of this connection were considered. Some properties of almost product structure, some properties of torsion tensor of product semi-symmetric connection and some relations between curvature tensors and almost product structure are given. Also, the paper checks a special case of such connection when its generator is a gradient vector.
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