Proceedings of the International Geometry Center最新文献_第6页

Infinite-dimensional manifolds related to C-spaces 与c空间相关的无限维流形

Proceedings of the International Geometry Center Pub Date : 2020-12-24 DOI: 10.15673/tmgc.v13i3.1856

M. Zarichnyi, O. Polivoda

引用次数: 0

On the generalization of Inoue manifolds 关于Inoue流形的推广

Proceedings of the International Geometry Center Pub Date : 2020-12-24 DOI: 10.15673/tmgc.v13i4.1748

A. Pajitnov, Endo Hisaaki

引用次数: 0

Galois coverings of one-sided bimodule problems 单侧双模问题的伽罗瓦覆盖

Proceedings of the International Geometry Center Pub Date : 2020-10-26 DOI: 10.15673/tmgc.v14i2.1768

V. Babych, N. Golovashchuk

引用次数: 0

A survey of homotopy nilpotency and co-nilpotency 同伦幂零和协幂零的综述

Proceedings of the International Geometry Center Pub Date : 2020-10-13 DOI: 10.15673/tmgc.v13i4.1750

Marek Golasinski

引用次数: 0

Topology of optimal flows with collective dynamics on closed orientable surfaces 封闭可定向表面上具有集体动力学的最优流拓扑

Proceedings of the International Geometry Center Pub Date : 2020-09-13 DOI: 10.15673/TMGC.V13I2.1731

A. Prishlyak, M. V. Loseva

引用次数: 19

Laplacian, on the Arrowhead Curve 在箭头曲线上的拉普拉斯

Proceedings of the International Geometry Center Pub Date : 2020-08-12 DOI: 10.15673/tmgc.v13i2.1746

Claire David

{"title":"Laplacian, on the Arrowhead Curve","authors":"Claire David","doi":"10.15673/tmgc.v13i2.1746","DOIUrl":"https://doi.org/10.15673/tmgc.v13i2.1746","url":null,"abstract":"\u0000In terms of analysis on fractals, the Sierpinski gasket stands out as one of the most studied example. \u0000The underlying aim of those studies is to determine a differential operator equivalent to the classic Laplacian. \u0000The classically adopted approach is a bidimensional one, through a sequence of so-called prefractals, i.e. a sequence of graphs that converges towards the considered domain. \u0000The Laplacian is obtained through a weak formulation, by means of Dirichlet forms, built by induction on the prefractals. \u0000 \u0000It turns out that the gasket is also the image of a Peano curve, the so-called Arrowhead one, obtained by means of similarities from a starting point which is the unit line. \u0000This raises a question that appears of interest. Dirichlet forms solely depend on the topology of the domain, and not of its geometry. \u0000Which means that, if one aims at building a Laplacian on a fractal domain as the aforementioned curve, the topology of which is the same as, for instance, a line segment, one has to find a way of taking account its specific geometry. \u0000 \u0000Another difference due to the geometry, is encountered may one want to build a specific measure. \u0000For memory, the sub-cells of the Kigami and Strichartz approach are triangular and closed: the similarities at stake in the building of the Curve called for semi-closed trapezoids. \u0000As far as we know, and until now, such an approach is not a common one, and does not appear in such a context. \u0000 \u0000It intererestingly happens that the measure we choose corresponds, in a sense, to the natural counting measure on the curve. \u0000Also, it is in perfect accordance with the one used in the Kigami and Strichartz approach. \u0000In doing so, we make the comparison -- and the link -- between three different approaches, that enable one to obtain the Laplacian on the arrowhead curve: the natural method; the Kigami and Strichartz approach, using decimation; the Mosco approach. \u0000 \u0000 \u0000 ","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"PP 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84346848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Hamiltonian operators and related differential-algebraic Balinsky-Novikov, Riemann and Leibniz type structures on nonassociative noncommutative algebras 非结合非交换代数上的哈密顿算子及相关的微分代数Balinsky-Novikov、Riemann和Leibniz型结构

Proceedings of the International Geometry Center Pub Date : 2019-12-28 DOI: 10.15673/tmgc.v12i4.1554

O. Artemovych, A. Balinsky, A. Prykarpatski

{"title":"Hamiltonian operators and related differential-algebraic Balinsky-Novikov, Riemann and Leibniz type structures on nonassociative noncommutative algebras","authors":"O. Artemovych, A. Balinsky, A. Prykarpatski","doi":"10.15673/tmgc.v12i4.1554","DOIUrl":"https://doi.org/10.15673/tmgc.v12i4.1554","url":null,"abstract":"We review main differential-algebraic structures lying in background of analytical constructing multi-component Hamiltonian operators as derivatives on suitably constructed loop Lie algebras, generated by nonassociative noncommutative algebras. The related Balinsky-Novikov and Leibniz type algebraic structures are derived, a new nonassociative \"Riemann\" algebra is constructed, deeply related with infinite multi-component Riemann type integrable hierarchies. An approach, based on the classical Lie-Poisson structure on coadjoint orbits, closely related with those, analyzed in the present work and allowing effectively enough construction of Hamiltonian operators, is also briefly revisited. As the compatible Hamiltonian operators are constructed by means of suitable central extentions of the adjacent weak Lie algebras, generated by the right Leibniz and Riemann type nonassociative and noncommutative algebras, the problem of their description requires a detailed investigation both of their structural properties and finite-dimensional representations of the right Leibniz algebras defined by the corresponding structural constraints. Subject to these important aspects we stop in the work mostly on the structural properties of the right Leibniz algebras, especially on their derivation algebras and their generalizations. We have also added a short Supplement within which we revisited the classical Poisson manifold approach, closely related to our construction of Hamiltonian operators, generated by nonassociative and noncommutative algebras. In particular, we presented its natural and simple generalization allowing effectively to describe a wide class of Lax type integrable nonlinear Kontsevich type Hamiltonian systems on associative noncommutative algebras.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86525234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

On fractal properties of Weierstrass-type functions weierstrass型函数的分形性质

Proceedings of the International Geometry Center Pub Date : 2019-10-19 DOI: 10.15673/tmgc.v12i2.1485

Claire David

引用次数: 2

Додатні ряди, множини підсум яких є канторвалами

Proceedings of the International Geometry Center Pub Date : 2019-10-15 DOI: 10.15673/tmgc.v12i2.1455

Ярослав Виннишин, Віта Маркітан, Микола Вікторович Працьовитий, І. Г. Савченко

引用次数: 2

A (CHR)3-flat trans-Sasakian manifold 一种(CHR)三平面跨sasakian歧管

Proceedings of the International Geometry Center Pub Date : 2019-09-21 DOI: 10.15673/tmgc.v12i2.1438

Koji Matsumoto

{"title":"A (CHR)3-flat trans-Sasakian manifold","authors":"Koji Matsumoto","doi":"10.15673/tmgc.v12i2.1438","DOIUrl":"https://doi.org/10.15673/tmgc.v12i2.1438","url":null,"abstract":"In [4] M. Prvanovic considered several curvaturelike tensors \u0000defined for Hermitian manifolds. Developing her ideas in [3], we defined in an almost contact Riemannian manifold another new curvaturelike tensor field, which is called a contact holomorphic Riemannian curvature tensor or briefly (CHR)3-curvature tensor. Then, we mainly researched (CHR)3-curvature tensor in a Sasakian manifold. Also we proved, that a conformally (CHR)3-flat Sasakian manifold does not exist. In the present paper, we consider this tensor field in a trans-Sasakian manifold. We calculate the (CHR)3-curvature tensor in a trans-Sasakian manifold. Also, the (CHR)3-Ricci tensor ρ3 and the (CHR)3-scalar curvature τ3 in a trans-Sasakian manifold have been obtained. Moreover, we define the notion of the (CHR)3-flatness in an almost contact Riemannian manifold. Then, we consider this notion in a trans-Sasakian manifold and determine the curvature tensor, the Ricci tensor and the scalar curvature. We proved that a (CHR)3-flat trans-Sasakian manifold is a generalized ɳ-Einstein manifold. Finally, we obtain the expression of the curvature tensor with respect to the Riemannian metric g of a trans-Sasakian manifold, if the latter is (CHR)3-flat.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88311447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0