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Academic literature on the topic 'Nijenhuis'

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Published: 10 March 2023

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Journal articles on the topic "Nijenhuis"

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Gozzi, E., and D. Mauro. "A new look at the Schouten–Nijenhuis, Frölicher–Nijenhuis, and Nijenhuis–Richardson brackets." Journal of Mathematical Physics 41, no. 4 (April 2000): 1916–33. http://dx.doi.org/10.1063/1.533218.

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Leroux, Philippe. "Construction of Nijenhuis operators and dendriform trialgebras." International Journal of Mathematics and Mathematical Sciences 2004, no. 49 (2004): 2595–615. http://dx.doi.org/10.1155/s0161171204402117.

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We construct Nijenhuis operators from particular bialgebras called dendriform-Nijenhuis bialgebras. It turns out that such Nijenhuis operators commute withTD-operators, a kind of Baxter-Rota operators, and are therefore closely related to dendriform trialgebras. This allows the construction of associative algebras, called dendriform-Nijenhuis algebras, made out of nine operations and presenting an exotic combinatorial property. We also show that the augmented free dendriform-Nijenhuis algebra and its commutative version have a structure of connected Hopf algebras. Examples are given.
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Bolsinov, Alexey V., Andrey Yu Konyaev, and Vladimir S. Matveev. "Nijenhuis geometry." Advances in Mathematics 394 (January 2022): 108001. http://dx.doi.org/10.1016/j.aim.2021.108001.

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Liu, Jiefeng, Sihan Zhou, and Lamei Yuan. "Conformal r-matrix-Nijenhuis structures, symplectic-Nijenhuis structures, and ON-structures." Journal of Mathematical Physics 63, no. 10 (October 1, 2022): 101701. http://dx.doi.org/10.1063/5.0101471.

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In this paper, we first study infinitesimal deformations of a Lie conformal algebra and a Lie conformal algebra with a module (called an [Formula: see text] pair), which lead to the notions of the Nijenhuis operator on the Lie conformal algebra and the Nijenhuis structure on the [Formula: see text] pair, respectively. Then, by adding compatibility conditions between Nijenhuis structures and [Formula: see text]-operators, we introduce the notion of an [Formula: see text]-structure on an [Formula: see text] pair and show that an [Formula: see text]-structure gives rise to a hierarchy of pairwise compatible [Formula: see text]-operators. In particular, we show that compatible [Formula: see text]-operators on a Lie conformal algebra can be characterized by Nijenhuis operators on Lie conformal algebras. Finally, we introduce the notions of the conformal r-matrix-Nijenhuis structure and symplectic-Nijenhuis structure on Lie conformal algebras and study their relations.
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CORDEIRO, FLÁVIO, and JOANA M. NUNES DA COSTA. "REDUCTION AND CONSTRUCTION OF POISSON QUASI-NIJENHUIS MANIFOLDS WITH BACKGROUND." International Journal of Geometric Methods in Modern Physics 07, no. 04 (June 2010): 539–64. http://dx.doi.org/10.1142/s0219887810004439.

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We extend the Falceto–Zambon version of Marsden–Ratiu Poisson reduction to Poisson quasi-Nijenhuis structures with background on manifolds. We define gauge transformations of Poisson quasi-Nijenhuis structures with background, study some of their properties and show that they are compatible with reduction procedure. We use gauge transformations to construct Poisson quasi-Nijenhuis structures with background.
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Wang, Qi, Jiefeng Liu, and Yunhe Sheng. "Koszul–Vinberg structures and compatible structures on left-symmetric algebroids." International Journal of Geometric Methods in Modern Physics 17, no. 13 (October 13, 2020): 2050199. http://dx.doi.org/10.1142/s0219887820501996.

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In this paper, we introduce the notion of Koszul–Vinberg–Nijenhuis (KVN) structures on a left-symmetric algebroid as analogues of Poisson–Nijenhuis structures on a Lie algebroid, and show that a KVN-structure gives rise to a hierarchy of Koszul–Vinberg structures. We introduce the notions of [Formula: see text]-structures, pseudo-Hessian–Nijenhuis structures and complementary symmetric [Formula: see text]-tensors for Koszul–Vinberg structures on left-symmetric algebroids, which are analogues of [Formula: see text]-structures, symplectic-Nijenhuis structures and complementary [Formula: see text]-forms for Poisson structures. We also study the relationships between these various structures.
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Wang, Qi, Yunhe Sheng, Chengming Bai, and Jiefeng Liu. "Nijenhuis operators on pre-Lie algebras." Communications in Contemporary Mathematics 21, no. 07 (October 10, 2019): 1850050. http://dx.doi.org/10.1142/s0219199718500505.

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First we use a new approach to define a graded Lie algebra whose Maurer–Cartan elements characterize pre-Lie algebra structures. Then using this graded Lie bracket, we define the notion of a Nijenhuis operator on a pre-Lie algebra which generates a trivial deformation of this pre-Lie algebra. There are close relationships between [Formula: see text]-operators, Rota–Baxter operators and Nijenhuis operators on a pre-Lie algebra. In particular, a Nijenhuis operator “connects” two [Formula: see text]-operators on a pre-Lie algebra whose any linear combination is still an [Formula: see text]-operator in certain sense and hence compatible [Formula: see text]-dendriform algebras appear naturally as the induced algebraic structures. For the case of the dual representation of the regular representation of a pre-Lie algebra, there is a geometric interpretation by introducing the notion of a pseudo-Hessian–Nijenhuis structure which gives rise to a sequence of pseudo-Hessian and pseudo-Hessian–Nijenhuis structures. Another application of Nijenhuis operators on pre-Lie algebras in geometry is illustrated by introducing the notion of a para-complex structure on a pre-Lie algebra and then studying para-complex quadratic pre-Lie algebras and para-complex pseudo-Hessian pre-Lie algebras in detail. Finally, we give some examples of Nijenhuis operators on pre-Lie algebras.
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De Nicola, Antonio, Juan Carlos Marrero, and Edith Padrón. "Reduction of Poisson–Nijenhuis Lie algebroids to symplectic-Nijenhuis Lie algebroids with a nondegenerate Nijenhuis tensor." Journal of Physics A: Mathematical and Theoretical 44, no. 42 (October 4, 2011): 425206. http://dx.doi.org/10.1088/1751-8113/44/42/425206.

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Norris, L. K. "Schouten–Nijenhuis brackets." Journal of Mathematical Physics 38, no. 5 (May 1997): 2694–709. http://dx.doi.org/10.1063/1.531981.

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Longguang, He, and Liu Baokang. "Dirac-Nijenhuis manifolds." Reports on Mathematical Physics 53, no. 1 (February 2004): 123–42. http://dx.doi.org/10.1016/s0034-4877(04)90008-0.

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Dissertations / Theses on the topic "Nijenhuis"

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Strohmayer, Henrik. "Prop profiles of compatible Poisson and Nijenhuis structures." Doctoral thesis, Stockholm : Department of Mathematics, Stockholm University, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-27262.

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Lavandier, Jean. "Role du tenseur de Nijenhuis dans l'intégralité de certaines g-structures." Toulouse 3, 1991. http://www.theses.fr/1991TOU30272.

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On etudie la nature du role du tenseur de nijenhuis dans l'integrabilite des g-structures definies par une 1-forme, 0-deformable. On donne une condition algebrique pour que la nullite du tenseur de nijenhuis soit equivalente a l'integrabilite de la structure, et on caracterise les structures satisfaisant a cette condition. Dans le cas ou la condition algebrique donnee precedemment n'est pas satisfaite, on met en evidence un tenseur dont la nullite equivaut a l'egalite du tenseur de structure avec le tenseur de nijenhuis
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Gérard, Maxime. "Méthodes de sélection de structures presque complexes dans le cadre symplectique." Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0051/document.

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Étant donné une variété symplectique $(M,\omega)$, il existe toujours des structures presque complexes $\omega$-compatibles positives. La question qui nous intéresse est de trouver des méthodes de sélection de certaines de ces structures. Des réponses ont déjà été données par V. Apostolov et T.Draghici, J.G. Evans, et J. Keller et M. Lejmi. Nous nous intéressons ici principalement à des méthodes de sélection définies en termes du tenseur de Nijenhuis. De manière très générale, lorsqu'on veut sélectionner certaines données géométriques, on peut aborder le problème de différentes manières. L’une d’entre elles consiste à regarder la décomposition en composantes irréductibles de certains tenseurs naturellement associés à la structure considérée et poser des conditions sur certaines composantes. Nous avons montré que le tenseur de Nijenhuis est irréductible sous l'action du groupe unitaire. Cette irréductibilité ne nous permet pas d'imposer d'autre condition linéaire à ce tenseur que son annulation, qui correspond aux variétés de Kähler. Une autre méthode possible de sélection est d’imposer des conditions à certaines distributions liées au problème. Nous avons étudié des distributions liées au tenseur de Nijenhuis. Nous nous sommes intéressés ici aux dimensions et propriétés d’involutivité possibles de ces distributions. Nous donnons des exemples invariants sous l’action d’un groupe, construits sur des groupes symplectiques ou sur des fibrés de twisteurs sur une variété riemannienne. La dernière méthode envisagée dans ce travail est la considération de fonctionnelles définies à partir des données. Pour construire une fonctionnelle la plus simple possible en termes du tenseur de Nijenhuis, nous intégrons une fonction polynomiale du second degré en les composantes du tenseur de Nijenhuis. On montre qu’un tel polynôme est toujours un multiple de la norme au carré de ce tenseur. La fonctionnelle obtenue est celle étudiée par Evans. Elle est a priori peu intéressante pour notre problème de sélection car il a prouvé qu’on peut trouver des exemples de variétés symplectiques n’admettant aucune structure kählérienne mais telle que l’infimum de la fonctionnelle soit nul
Given a symplectic manifold $(M,\omega)$, there always exist almost complex $\omega,$-compatible positive structures. The problem studied in this thesis is to find methods to select some of these structures. Answers have already been suggested by V. Apostolov and T.Draghici, J. G. Evans, and J. Keller and M. Lejmi. We are mainly interested here in selection methods defined in terms of the Nijenhuis tensor. The problem of selecting geometric objects can be tackled in various ways. One of them is to decompose into irreducible components some tensors naturally associated with the structure, and to impose conditions on some of those components. We prove that the Nijenhuis tensor is irreducible under the action of the unitary group. This irreducibility does not allow to impose any linear condition on the Nijenhuis tensor, except the vanishing of it, which corresponds to Kähler manifolds. Another possible method of selection is to impose conditions on distributions related to the problem. We study distributions defined by the Nijenhuis tensor. Our results concern the possible dimensions and properties of involutivity of these distributions. We give examples which are invariant under the action of a group, on some symplectic groups and on twisted bundles over some Riemannian manifolds. The last method considered in this work consists in looking for extremals of functionals defined from the data. To construct the simplest functional defined in terms of the Nijenhuis tensor, we integrate a polynomial function of the second degree into the components of this tensor. All such polynomials are multiple of the square of the norm of this tensor. This functional is the one studied by Evans; the drawback for our selection problem is that there exist examples of compact symplectic manifolds which do not admit any K\"ahler structure but such that the infimum of the functional is zero
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Wei, Xi [Verfasser], Gabriele [Gutachter] Diekert, Ivonne [Gutachter] Nijenhuis, and Ulrich [Gutachter] Szewzyk. "Characterization of the biochemistry and physiology of hydrocarbon degradation pathways by stable isotope approaches / Xi Wei ; Gutachter: Gabriele Diekert, Ivonne Nijenhuis, Ulrich Szewzyk." Jena : Friedrich-Schiller-Universität Jena, 2018. http://d-nb.info/1170588352/34.

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Nijenhuis, Ivonne [Verfasser], R. Gary [Akademischer Betreuer] Sawers, G. [Akademischer Betreuer] Diekert, and Lollar B. [Akademischer Betreuer] Sherwood. "Characterisation of microbial transformation of halogenated organic contaminants using compound-specific stable isotope analysis / Ivonne Nijenhuis. Betreuer: R. Gary Sawers ; G. Diekert ; B. Sherwood Lollar." Halle, Saale : Universitäts- und Landesbibliothek Sachsen-Anhalt, 2016. http://d-nb.info/109078662X/34.

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Marshall, David G. "Classification of integrable hydrodynamic chains using the Haantjes tensor." Thesis, Loughborough University, 2008. https://dspace.lboro.ac.uk/2134/14547.

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The integrability of an m-component system of hydrodynamic type, Ut = v(u)ux, by the generalized hodograph method requires the diagonalizability of the m x m matrix v(u). The diagonalizability is known to be equivalent to the vanishing of the corresponding Haantjes tensor. This idea is applied to hydrodynamic chains - infinite-component systems of hydrodynamic type for which the 00 x 00 matrix v(u) is 'sufficiently sparse'. For such 'sparse' systems the Haantjes tensor is well-defined, and the calculation of its components involves only a finite number of summations. The calculation of the Haantjes tensor is done by using Mathematica to perform symbolic calculations. Certain conservative and Hamiltonian hydrodynamic chains are classified by setting Haantjes tensor equal to zero and solving the resulting system of equations. It is shown that the vanishing of the Haantjes tensor is a necessary condition for a hydrodynamic chain to possess an infinity of semi-Hamiltonian hydrodynamic reductions, thus providing an easy-to-verify necessary condition for the integrability of such sysyems. In the cases of the Hamiltonian hydrodynamic chains we were able to first construct one extra conservation law and later a generating function for conservation laws, thus establishing the integrability.
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Renpenning, Julian [Verfasser], Peter [Akademischer Betreuer] Neubauer, Ivonne [Akademischer Betreuer] Nijenhuis, Juri [Akademischer Betreuer] Rappsilber, Hans-Hermann [Akademischer Betreuer] Richnow, and Lorenz [Akademischer Betreuer] Adrian. "Characterization of microbial reductive dehalogenation using novel compound-specific stable isotope analyses / Julian Renpenning. Betreuer: Peter Neubauer ; Ivonne Nijenhuis. Gutachter: Peter Neubauer ; Juri Rappsilber ; Hans-Hermann Richnow ; Lorenz Adrian." Berlin : Technische Universität Berlin, 2015. http://d-nb.info/1078310467/34.

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Šramková, Kristína. "Frölicherova-Nijenhuisova závorka a její aplikace v geometrii a variačním počtu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-382475.

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This Master's thesis clarifies the significance of Frölicher-Nijenhuis bracket and its applications in problems of physics. The basic apparatus for these applications is differential geometry on manifolds, tensor calculus and differential forms, which are contained in the first part of the thesis. The second part summarizes the basic theory of calculus of variations on manifolds and its selected applications in the field of physics. The last part of the thesis is devoted to the applications of Frölicher-Nijenhuis bracket in the derivation of Maxwell's equations and to the description of the geometry of ordinary differential equations.
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Azimi, Mohammad Jawad. "Higher structures: gerbes and Nijenhuis forms." Doctoral thesis, 2013. http://hdl.handle.net/10316/23739.

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Tese de doutoramento em Matemática apresentada à Faculdade de Ciências e Tecnologia da Universidade de Coimbra
The thesis is devoted to higher structures, which is a generic name for all those collections of $n$-ary brackets or products reducing for $n=2$ to the ordinary ones. Among examples of those are $2$-groups, and their related notions of principal bundles, i.e. non-Abelian gerbes, and $L_\infty$-structures. These two major examples are the central objects of the two chapters of the present work. In the first chapter, we give a precise and general description of gerbes valued in arbitrary crossed module and over an arbitrary differential stack. We do it using only Lie groupoids, hence ordinary differential geometry, by considering differential stacks as being Lie groupoids up to Morita equivalence. We prove the coincidence with the existing notions by comparing our construction with non-Abelian cohomology. More precisely, we introduce the key notion of extension of Lie groupoids valued in a crossed-module. We relate it with Dedecker's non-Abelian $1$-cocycles, and we then show that Morita equivalence amounts to co-boundaries, paving the way for a general definition of gerbes valued in a crossed-module over a differential stack. In the second chapter, we develop the theory of Nijenhuis forms on $L_\infty$-algebras. First, we recall a convenient notion of Richardson-Nijenhuis bracket on the graded symmetric vector valued forms on a graded vector space, bracket for which $L_{\infty}$-algebras are simply Poisson elements. Weak Nijenhuis vector valued forms for a given $L_{\infty}$-algebra are defined to be forms of degree $0$ deforming (i.e. taking bracket) that Poisson element into an other Poisson element. Nijenhuis forms are those forms ${\mathcal N}$ for which deforming twice by ${\mathcal N}$ is like deforming once by a form ${\mathcal K}$ called the square of ${\mathcal N }$. We obtain in this context an infinite hierarchy of $L_{\infty}$-algebras. Among examples of such Nijenhuis deformations are the Euler map on an arbitrary $L_{\infty}$-algebra or Poisson and Maurer Cartan elements on a differential graded Lie algebra. A classification of Nijenhuis forms on anchor-free Lie $2$-algebras can be completed. We also show that there is, under adequate conditions, a one to one correspondence between the Nijenhuis vector valued forms $\mathcal{N}$ with respect to the Lie $2$-algebra associated to a Courant algebroid and Nijenhuis $\mathcal{C}^{\infty}$-linear maps on the Courant algebroid itself. We give examples of Nijenhuis vector valued forms on the Lie $n$-algebras associated to $n$-plectic manifolds. We also explain how Nijenhuis tensors on a Lie algebroid are indeed Nijenhuis forms of some Gerstenhaber algebra, considered as an $L_\infty$-algebra. For the latter $L_{\infty}$-algebra structure, moreover, $\Omega N$-structures and Poisson-Nijenhuis structrures can also be seen as Nijenhuis forms.
Esta tese trata de estruturas de ordem superior, designação genérica para todas as coleções de parêntesis ou produtos n-uplos que, no caso de n = 2, se reduzem aos usuais. Exemplos destas estruturas incluem os 2-grupos e as noções com eles relacionadas de brados principais, isto é, gerbes não-Abelianos, e estruturas L1. Estes dois exemplos importantes são os objetos centrais dos dois capítulos desta dissertação. No primeiro capítulo, apresentamos uma descrição geral e precisa de gerbes com valores em módulos cruzados arbitrários e sobre stacks diferenciais arbitrários. Para esta descrição usamos grupóides de Lie, ou seja, apenas geometria diferencial clássica, considerando os stacks diferenciais como sendo grupóides de Lie, módulo equivalência de Morita. Provamos que a descrição apresentada conduz a uma noção que é equivalente às já existentes, comparando a nossa construção com a cohomologia não-Abeliana. Mais exatamente, introduzimos a noção chave de extensão de grupóide de Lie com valores num módulo cruzado, relacionamo-la com 1-cociclos não-Abelianos de Dedecker e provamos, em seguida, que a equivalência de Morita se traduz em cobordos, abrindo assim o caminho para uma de nição geral de gerbes com valores num módulo cruzado sobre um stack diferencial. No segundo capítulo, desenvolvemos a teoria de formas de Nijenhuis em álgebras L1. Começamos por apresentar uma de nição de parênteses de Richardson-Nijenhuis para formas simétricas graduadas a valores vetoriais, num espaço vetorial graduado. Para este parênteses, as estruturas L1 são simplesmente elementos de tipo Poisson. Dada uma álgebra L1, uma forma a valores vetoriais, de grau zero, que deforma um elemento de Poisson num outro elemento de Poisson, diz-se uma forma fraca de Nijenhuis. Aqui, a deformação consiste em tomar o parênteses da forma fraca de Nijenhuis com o elemento. As formas de Nijenhuis N são aquelas para as quais deformar duas vezes por N é o mesmo que deformar uma vez por uma forma K, que é dita o quadrado de N. Neste contexto, obtemos uma hierarquia in nita de álgebras L1. De entre os exemplos de deformações de Nijenhuis, contam-se a aplicação de Euler numa álgebra L1 arbitrária, bem como os elementos de Poisson e de Maurer Cartan numa álgebra de Lie diferencial graduada. Efetuamos a classi cação das formas de Nijenhuis em 2-álgebras de Lie com âncora nula. Mostramos também que, sobre certas condições, existe uma correspondência biunívoca entre as formas de Nijenhuis a valores vetoriais, na 2-álgebra de Lie associada a um algebr óide de Courant, e as aplicações de Nijenhuis C1-lineares no mesmo algebróide de Courant. Apresentamos exemplos de formas de Nijenhuis a valores vetoriais nas n-álgebras de Lie associadas a variedades n-pléticas. Explicamos também como tensores de Nijenhuis num algebróide de Lie podem ser vistos como formas de Nijenhuis numa certa álgebra de Gerstenhaber, considerada como álgebra L1. Além disso, para esta última estrutura de álgebra L1, estruturas N e estruturas de Poisson-Nijenhuis podem também ser vistas como formas de Nijenhuis.
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Viviani, Emanuele. "Bihamiltonian structures on compact hermitian symmetric spaces." Doctoral thesis, 2022. http://hdl.handle.net/2158/1268162.

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In this thesis, we discuss a new approach to the problem of the diagonalization of the Nijenhuis tensor on compact hermitian symmetric spaces. Our attention is more focused on the hamiltonian forms rather than on the eigenvalues of the Nijenhuis tensor. This is motivated by the fact that the eigenvalues of N are only continuous functions and their derivatives have singularities. We describe these hamiltonian forms in terms of polynomials invariant with respect to a chain of subalgebra.
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Books on the topic "Nijenhuis"

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Stedelijk Museum de Lakenhal (Leiden), ed. Leidse ateliers: Peter Duivenvoorden, Herby Nijenhuis,Rob van't Zelfde. Leiden: Stedelijk Museum de Lakenhal, 1987.

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Werkman, Hans. Spitten en [niet] moe worden: Leven en werk van Bé Nijenhuis 1914-1972. Kampen: Kok, 1995.

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1978-, Storms Martijn, ed. De Nederlandse cartografie van Latijns Amerika: Kaarten uit de collectie Van Keulen en de collectie Bodel Nijenhuis = A cartografia neerlandesa da América Latina : mapas da coleção Van Keulen e da coleção Bodel Nijenhuis. Leiden: Universiteitsbibliotheek Leiden, 2008.

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Willem, Nijenhuis, Jong, Christiaan G. F. de., and Sluis Jacob van 1953-, eds. Gericht verleden: Kerkhistorische opstellen aangeboden aan prof. dr. W. Nijenhuis ter gelegenheid van zijn vijfenzeventigste verjaardag = essays on church history dedicated to prof. dr. W. Nijenhuis on the occasion of his 75th birthday. Leiden: J.J. Groen, 1991.

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Bodel Nijenhuis, Johannes Tiberius, 1797-1872, Lem Anton van der, Ommen Kasper van, Schaeps J, and Rijksuniversiteit te Leiden Bibliotheek, eds. De verzamelingen van Bodel Nijenhuis: Kaarten portretten en boeken van een pionier in de historische cartografie. Leiden: Universiteitsbibliotheek Leiden, 2008.

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de, Vries Dolf, Rijksuniversiteit te Leiden. Bibliotheek. Collectie Bodel Nijenhuis., and International Conference on the History of Cartography (13th : 1989 : Amsterdam, Netherlands), eds. Kaarten met geschiedenis, 1500-1800: Een selectie van oude getekende kaarten van Nederland vit de Collectie Bodel Nijenhuis. Utrecht: H&S, HES uitgevers, 1989.

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Book chapters on the topic "Nijenhuis"

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Aoyama, Hideaki, Anatoli Konechny, V. Lemes, N. Maggiore, M. Sarandy, S. Sorella, Steven Duplij, et al. "Nijenhuis Tensor." In Concise Encyclopedia of Supersymmetry, 264. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_346.

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Vaisman, Izu. "A Lecture on Poisson—Nijenhuis Structures." In Integrable Systems and Foliations, 169–85. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-4134-8_10.

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Mikami, Kentaro. "An Interpretation of the Schouten-Nijenhuis Bracket." In Noncommutative Differential Geometry and Its Applications to Physics, 131–43. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0704-7_8.

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Vaisman, Izu. "The Poisson Bivector and the Schouten-Nijenhuis Bracket." In Lectures on the Geometry of Poisson Manifolds, 5–17. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8495-2_2.

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Ouzilou, R. "Quelques remarques sur les variétés de Poisson-Nijenhuis." In Symplectic Geometry and Mathematical Physics, 355–65. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4757-2140-9_17.

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Kawai, Kotaro, Hông Vân Lê, and Lorenz Schwachhöfer. "Frölicher–Nijenhuis Bracket on Manifolds with Special Holonomy." In Lectures and Surveys on G2-Manifolds and Related Topics, 201–15. New York, NY: Springer US, 2020. http://dx.doi.org/10.1007/978-1-0716-0577-6_8.

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Magri, F., and T. Marsico. "Poisson-Nijenhuis Manifolds, Classical Yang-Baxter Equations, and Frobenius Algebras." In Springer Proceedings in Physics, 275–87. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-24748-5_15.

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de Jesús Cruz Guzmán, José, and Zbigniew Oziewicz. "Symbolic Calculation for Frölicher-Nijenhuis $\mathbb R $ -Algebra for Exploring in Electromagnetic Field Theory." In Computational Science - ICCS 2004, 552–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24687-9_70.

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9

"Nijenhuis-Richardson algebra and Fro¨licher-Nijenhuis Lie module." In Non-Associative Algebra and Its Applications, 145–64. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420003451-17.

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Guzm√°n, Jos√©de Jes√∫s Cruz, and Zbigniew Oziewicz. "Nijenhuis-Richardson algebra and Fr√∂licher-Nijenhuis Lie module." In Lecture Notes in Pure and Applied Mathematics, 109–27. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420003451.ch9.

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Conference papers on the topic "Nijenhuis"

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Golovko, Valentina. "Variational Poisson–Nijenhuis structures for evolution PDEs." In Proceedings of the International Conference on SPT 2007. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812776174_0036.

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Reports on the topic "Nijenhuis"

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Yanovski, Alexander B. Poisson-Nijenhuis Structure for Generalized Zakharov-Shabat System in Pole Gauge on the Lie Algebra $\mathfrak{sl}(3,\mathbb{C})$. GIQ, 2012. http://dx.doi.org/10.7546/giq-12-2011-342-353.

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