Proceedings of the International Geometry Center最新文献_第8页

A Physics-Based Estimation of Mean Curvature Normal Vector for Triangulated Surfaces 基于物理的三角曲面平均曲率法向量估计

Proceedings of the International Geometry Center Pub Date : 2019-02-06 DOI: 10.15673/tmgc.v12i1.1377

S. Das, M. Cenanovic, Junfeng Zhang

引用次数: 1

Warped product semi-slant submanifolds in locally conformal Kaehler manifolds II 局部共形Kaehler流形中的翘曲积半倾斜子流形II

Proceedings of the International Geometry Center Pub Date : 2019-01-21 DOI: 10.15673/TMGC.V11I3.1202

Koji Matsumoto

{"title":"Warped product semi-slant submanifolds in locally conformal Kaehler manifolds II","authors":"Koji Matsumoto","doi":"10.15673/TMGC.V11I3.1202","DOIUrl":"https://doi.org/10.15673/TMGC.V11I3.1202","url":null,"abstract":"In 1994 N.~Papaghiuc introduced the notion of semi-slant submanifold in a Hermitian manifold which is a generalization of $CR$- and slant-submanifolds, cite{MR0353212}, cite{MR760392}. \u0000In particular, he considered this submanifold in Kaehlerian manifolds, cite{MR1328947}. \u0000Then, in 2007, V.~A.~Khan and M.~A.~Khan considered this submanifold in a nearly Kaehler manifold and obtained interesting results, cite{MR2364904}. \u0000Recently, we considered semi-slant submanifolds in a locally conformal Kaehler manifold and we gave a necessary and sufficient conditions of the two distributions (holomorphic and slant) be integrable. \u0000Moreover, we considered these submanifolds in a locally conformal Kaehler space form. \u0000In the last paper, we defined $2$-kind warped product semi-slant submanifolds in almost hermitian manifolds and studied the first kind submanifold in a locally conformal Kaehler manifold. \u0000Using Gauss equation, we derived some properties of this submanifold in an locally conformal Kaehler space form, cite{MR2077697}, cite{MR3728534}. \u0000In this paper, we consider same submanifold with the parallel second fundamental form in a locally conformal Kaehler space form. \u0000Using Codazzi equation, we partially determine the tensor field $P$ which defined in~eqref{1.3}, see Theorem~ref{th4.1}. \u0000Finally, we show that, in the first type warped product semi-slant submanifold in a locally conformal space form, if it is normally flat, then the shape operators $A$ \u0000satisfy some special equations, see Theorem~ref{th5.2}.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89322273","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: 2

Про моногенні функції на розширеннях комутативної алгебри

Proceedings of the International Geometry Center Pub Date : 2019-01-21 DOI: 10.15673/TMGC.V11I3.1200

Віталій Станіславович Шпаківський

引用次数: 0

О регулярных тканях, определенных плюригармоническими функциями 由多项式函数定义的正则组织

Proceedings of the International Geometry Center Pub Date : 2019-01-21 DOI: 10.15673/TMGC.V11I3.1201

Любовь Михайловна Пиджакова, Александр Михайлович Шелехов

{"title":"О регулярных тканях, определенных плюригармоническими функциями","authors":"Любовь Михайловна Пиджакова, Александр Михайлович Шелехов","doi":"10.15673/TMGC.V11I3.1201","DOIUrl":"https://doi.org/10.15673/TMGC.V11I3.1201","url":null,"abstract":"Как известно, функция двух переменных z=f(x, y) задает на плоскости (x, y) в окрестности регулярной точки некоторую три-ткань, образованную слоениями x=const, y=const и f(x, y)=const. \u0000Три-ткань называется регулярной, если она эквивалентна (локально диффеоморфна) три-ткани, образованной тремя семействами параллельных прямых. \u0000В этом случае уравнение ткани имеет вид $z=fleft(alpha(x)+beta(y)right)$. \u0000В одной из работ авторов этой статьи были найдены все регулярные три-ткани, определяемые некоторыми известными уравнениями в частных производных, в частности, определяемые гармоническими функциями. \u0000В настоящей работе результаты обобщаются для плюригармонических функций вида \u0000u=f(x_1, ...., x_r, y_1, ... , y_r). \u0000Во-первых, функция такого вида определяет на многообразии размерности 2r (2r + 1)-ткань, образованную слоениями коразмерности 1 вида x_i=const, y_i=const, i=1, 2, ..., r и u=const. \u0000(2r + 1)-ткань называется регулярной, если в некоторых локальных координатах ее уравнение может быть записано в виде \u0000$$ \u0000u=fleft(varphi_1(x_1)+ldots + varphi_1(x_r)+psi_1(y_1)+ldots +psi_r( y_r)right). \u0000$$ \u0000В этой статье мы находим все плюригармонические функции, задающие регулярные (2r + 1)-ткани (теорема 1). \u0000С другой стороны, каждая плюригармоническая функция u=f(x_1,..., x_r, y_1, ... , y_r) \u0000определяет на 2r-мерном многообразии три-ткань W(r,r,2r-1), образованную двумя r-мерными слоениями x_i=const и y_i=const и слоением u=const коразмерности 1. \u0000Эта ткань называется регулярной, если в некоторых локальных координатах ее уравнение может быть записано в виде \u0000$$ \u0000u=fleft(varphi(x_1, x_2,ldots, x_r)+psi(y_1, y_2,ldots, y_r)right). \u0000$$ \u0000В этой работе найдены все плюригармонические функции, определяющие регулярные три-ткани W(r,r,2r-1) (теорема 2)","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90265931","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

Homotopy properties of smooth functions on the Möbius band Möbius带上光滑函数的同伦性质

Proceedings of the International Geometry Center Pub Date : 2019-01-11 DOI: 10.15673/tmgc.v12i3.1488

I. Kuznietsova, S. Maksymenko

引用次数: 2

On the generalization of the Darboux theorem 关于达布定理的推广

Proceedings of the International Geometry Center Pub Date : 2018-12-24 DOI: 10.15673/tmgc.v12i2.1436

K. Eftekharinasab

{"title":"On the generalization of the Darboux theorem","authors":"K. Eftekharinasab","doi":"10.15673/tmgc.v12i2.1436","DOIUrl":"https://doi.org/10.15673/tmgc.v12i2.1436","url":null,"abstract":"Darboux theorem to more general context of Frechet manifolds we face an obstacle: in general vector fields do not have local flows. Recently, Fr'{e}chet geometry has been developed in terms of projective limit of Banach manifolds. In this framework under an appropriate Lipchitz condition The Darboux theorem asserts that a symplectic manifold $(M^{2n},omega)$ is locally symplectomorphic to $(R^{2n}, omega_0)$, where $omega_0$ is the standard symplectic form on $R^{2n}$. This theorem was proved by Moser in 1965, the idea of proof, known as the Moser’s trick, works in many situations. The Moser tricks is to construct an appropriate isotopy $ ff_t $ generated by a time-dependent vector field $ X_t $ on $M$ such that $ ff_1^{*} omega = omega_0$. Nevertheless, it was showed by Marsden that Darboux theorem is not valid for weak symplectic Banach manifolds. However, in 1999 Bambusi showed that if we associate to each point of a Banach manifold a suitable Banach space (classifying space) via a given symplectic form then the Moser trick can be applied to obtain the theorem if the classifying space does not depend on the point of the manifold and a suitable smoothness condition holds. \u0000 If we want to try to generalize the local flows exist and with some restrictive conditions the Darboux theorem was proved by Kumar. In this paper we consider the category of so-called bounded Fr'{e}chet manifolds and prove that in this category vector fields have local flows and following the idea of Bambusi we associate to each point of a manifold a Fr'{e}chet space independent of the choice of the point and with the assumption of bounded smoothness on vector fields we prove the Darboux theorem.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"130 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73131705","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: 3

A calculation of periodic data of surface diffeomorphisms with one saddle orbit. 单鞍轨道表面微分同态的周期数据计算。

Proceedings of the International Geometry Center Pub Date : 2018-09-15 DOI: 10.15673/TMGC.V11I2.1025

Олена В'ячеславівна Ноздрінова, Ольга Віталіївна Починка

引用次数: 0

On measures of nonplanarity of cubic graphs 关于三次图非平面性的测度

Proceedings of the International Geometry Center Pub Date : 2018-09-15 DOI: 10.15673/TMGC.V11I2.1026

L. Plachta

引用次数: 0

Moyal and Rankin-Cohen deformations of algebras 代数的Moyal和Rankin-Cohen变形

Proceedings of the International Geometry Center Pub Date : 2018-09-15 DOI: 10.15673/TMGC.V11I2.1027

V. Lyubashenko

引用次数: 0

Trajectory equivalence of optimal Morse flows on closed surfaces 封闭表面上最优莫尔斯流的轨迹等价

Proceedings of the International Geometry Center Pub Date : 2018-06-10 DOI: 10.15673/TMGC.V11I1.916

Злата Кибалко, Олександр Олегович Пришляк, Roman Shchurko

引用次数: 20