Shaikh, Absos AliKim, Young HoGhosh, Pinaki Ranjan
6页
查看更多>>摘要：The present paper deals with some characterizations of rectifying and osculating curves on a smooth surface with respect to the reference frame {(T) over right arrow, (N) over right arrow, (T) over right arrow x (N) over right arrow}. We have computed the components of position vectors of rectifying and osculating curves along (T) over right arrow, (N) over right arrow, (T) over right arrow x (N) over right arrow($) over right arrow Nand then investigated their invariancy under isometry of surfaces, and it is shown that they are invariant iff either the normal curvature of the curve is invariant or the position vector of the curve is in the direction of the tangent vector to the curve. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We prove that the topological recursion formalism can be used to compute the WKB expansion of solutions of second order differential operators obtained by quantization of any hyper-elliptic curve. We express this quantum curve in terms of spectral Darboux coordinates on the moduli space of meromorphic sl2-connections on P1 and argue that the topological recursion produces a 2g-parameter family of associated tau functions, where 2g is the dimension of the moduli space considered. We apply this procedure to the 6 Painleve equations which correspond to g =1 and consider a g = 2 example. (c) 2021 Elsevier B.V. All rights reserved.
NSTL
Elsevier