作者：Jarosław Buczyński , Giovanni Moreno 来源：[J].Banach Center Publications, 2019, Vol.117, pp.145-176IMPAS 摘要：Complex contact manifolds arise naturally in differential geometry, algebraic geometry and exterior differential systems. Their classification would answer an important question about holonomy groups. The geometry of such manifold $X$ is governed by the contact lines contain...
 作者：Francesco Russo 来源：[J].Banach Center Publications, 2019, Vol.117, pp.113-144IMPAS 摘要：The aim of these notes is to introduce the basic notions of projective duality and of secant varieties in order to provide a firm background to the geometrical counterpart of the main results by Doubrov and Ferapontov [J. Geom. Phys. 60 (2010), 1604–1616] and Ferapontov, Had...
 作者：Andriy Panasyuk 来源：[J].Banach Center Publications, 2019, Vol.117, pp.177-210IMPAS 摘要：The aim of this paper is two-fold. First, a survey of the theory of Kronecker webs and their relations with bihamiltonian structures and PDEs is presented. Second, a partial solution to the problem of bisymplectic realization of a bihamiltonian structure is given. Both the goals ...
 作者：Benjamin McKay 来源：[J].Banach Center Publications, 2019, Vol.117, pp.45-55IMPAS 摘要：These lectures explain how to apply the Cartan–Kähler theorem to problems in differential geometry. We want to decide if there are submanifolds of a given dimension inside a given manifold on which given differential forms vanish. The Cartan–Kähler theorem gives a linea...
 作者：Jan Gutt , Gianni Manno , Giovanni Moreno 来源：[J].Banach Center Publications, 2019, Vol.117, pp.9-44IMPAS 摘要：This paper contains a thorough introduction to the basic geometric properties of the manifold of Lagrangian subspaces of a linear symplectic space, known as the Lagrangian Grassmannian. It also reviews the important relationship between hypersurfaces in the Lagrangian Grassm...
 作者：Emilio Musso , Lorenzo Nicolodi 来源：[J].Banach Center Publications, 2019, Vol.117, pp.223-255IMPAS 摘要：This exposition gives an introduction to the theory of surfacesin Laguerre geometry and surveys some significant results concerningthree important classes of surfaces in Laguerre geometry, namely$L$-isothermic, $L$-minimal, and generalized $L$-minimal surfaces.The quadric mo...
 作者：Gary R. Jensen 来源：[J].Banach Center Publications, 2019, Vol.117, pp.211-222IMPAS 摘要：These notes introduce Lie sphere geometry of surfaces in Euclidean 3-space.A similar article with a different point of view is:G. R. Jensen, Dupin hypersurfaces in Lie sphere geometry ,in: Geometry and Analysis on Manifolds, Progr. Math. 308, Birkhäuser/Springer, Cham, 2015,...
 作者：Abraham D. Smith 来源：[J].Banach Center Publications, 2019, Vol.117, pp.57-112IMPAS 摘要：This expository monograph cuts a short path from the common, elementary background in geometry (linear algebra, vector bundles, and algebraic ideals) to the most advanced theorems about involutive exterior differential systems: (1) The incidence correspondence of the charact...
 作者：Michael Filaseta , Robert Murphy , Andrew Vincent 来源：[J].Banach Center Publications, 2019, Vol.118, pp.245-259IMPAS 摘要：Let $f(x)$ be a polynomial with integer coefficients.If either $f(x) = x^{{\rm deg}\,{f}}f(1/x)$ or $f(x) = -x^{{\rm deg}\,{f}}f(1/x)$, then $f(x)$ is called reciprocal.We refer to the non-reciprocal part of $f(x)$ as the polynomial $f(x)$ removedof each of its irreducible recipr...
 作者：Arran Fernandez 来源：[J].Banach Center Publications, 2019, Vol.118, pp.113-124IMPAS 摘要：We derive and prove a new formulation of the Lerch zeta function as a fractional derivative of an elementary function. We demonstrate how this formulation interacts very naturally with basic known properties of Lerch zeta, and use the functional equation to obtain a second formul...