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Einstein Finsler metrics and Killing vector fields on Riemannian manifolds

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Science China Mathematics 2017年第1期60卷 83-98页

作者： CHENG XinYue shen zhongmin School of Mathematics and Statistics Chongqing University of Technology Department of Mathematical Sciences Indiana University-Purdue University

We use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on S^3 with Ric = 2F^2, Ric = 0 and Ric =-2F^2, respectively. This family of metrics provides an important class of Finsler metrics in dimension three, whose Ricci curvature is a constant, but the flag curvature is not.

关键词： Riemann流形度量和 Finsler度量向量场 Killing型爱因斯坦黎曼流形旗曲率

On conformal vector fields on Randers manifolds

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Science China Mathematics 2012年第9期55卷 1869-1882页

作者： shen zhongmin XIA QiaoLing Department of Mathematical Sciences Indiana University-Purdue University Indianapolis 46202-3216 USA Department of Mathematics Zhejiang University Hangzhou 310027 China

In this paper,we study conformal vector fields on a Randers manifold with certain curvature properties.In particular,we completely determine conformal vector fields on a Randers manifold of weakly isotropic flag curva... 详细信息

关键词：兰德斯向量场共形流形各向同性旗曲率矢量场

Diagenetic fluid evolution and water-rock interaction model of carbonate cements in sandstone: An example from the reservoir sandstone of the Fourth Member of the Xujiahe Formation of the Xiaoquan-Fenggu area, Sichuan Province, China

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Science China Earth Sciences 2014年第5期57卷 1077-1092页

作者： LIU SiBing HUANG SiJing shen zhongmin Lü ZhengXiang SONG RongCai State Key Laboratory of Oil-Gas Reservoirs Geology and Exploitation Chengdu University of Technology

Carbonate cement is the most abundant cement type in the Fourth Member of the Xujiahe Formation in the Xiaoquan-Fenggu area of the West Sichuan Depression. Here we use a systematic analysis of carbonate cement petrology, mineralogy, carbon and oxygen isotope ratios and enclosure homogenization temperatures to study the precipitation mechanism, pore fluid evolution, and distribution of different types of carbonate cement in reservoir sand in the study area. Crystalline calcite has relatively heavy carbon and oxygen isotope ratios(δ13C = 2.14‰, δ18O = -5.77‰), and was precipitated early. It was precipitated directly from supersaturated alkaline fluid under normal temperature and pressure conditions. At the time of precipitation, the fluid oxygen isotope ratio was very light, mainly showing the characteristics of a mixed meteoric water-seawater fluid(δ18O = -3‰), which shows that the fluid during precipitation was influenced by both meteoric water and seawater. The calcite cement that fills in the secondary pores has relatively lighter carbon and oxygen isotope ratios(δ13C = -2.36‰, δ18O = -15.68‰). This cement was precipitated late, mainly during the Middle and Late Jurassic. An important material source for this carbonate cement was the feldspar corrosion process that involved organic matter. The Ca2+, Fe3+ and Mg2+ ions released by the clay mineral transformation process were also important source materials. Because of water-rock interactions during the burial process, the oxygen isotope ratio of the fluid significantly increased during precipitation, by about 3‰. The dolomite cements in calcarenaceous sandstone that was precipitated during the Middle Jurassic have heavier carbon and oxygen isotope ratios, which are similar to those of carbonate debris in the sandstone(δ13C = 1.93‰, δ18O = -6.11‰), demonstrating that the two are from the same source that had a heavier oxygen isotope ratio(δ18O of about 2.2‰). The differences in fluid oxygen isotope ratios during cement precipitation reflect the influences of diff

关键词：碳酸盐胶结物水岩相互作用胶结砂岩流体演化须家河组相互作用模型储集层氧同位素比率

Geochemical characteristics of noble gases in natural gas and their application in tracing natural gas migration in the middle part of the western Sichuan Depression, China

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Petroleum Science 2013年第3期10卷 327-335页

作者： Wang Peng shen zhongmin Liu Sibing Lv Zhengxiang Zhu Tong Gong Yajun State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Chengdu University of Technology Geology Scientific Research Institute of shengli Oilfield Branch Company SINOPEC

Noble gases in natural gas, from Xiaoquan, Xinchang, Hexingchang and Fenggu gas reservoirs in the middle part of the western Sichuan Depression, China, were analysed. Results show that the volume content of crustal noble gases accounts for 97.9% to 99.7% of the total noble gas content, indicating that the noble gases in the study area are very largely derived from the crust. Moreover, the 40Ar time-accumulating effect of source rocks is used to determine the complex relationship between gases and source rocks in this area, and the results agree well with that from analysis of source rock light hydrocarbons. Due to the short migration distance, the separation of 4He and 40Ar is not significant in Xujiahe natural gas and Lower and Middle Jurassic natural gas, so it is difficult to trace natural gas migration. However, this separation characteristic of 4He and 40Ar in Middle and Upper Jurassic natural gas is significant, which indicates that natural gas migration was from the Middle Jurassic to Upper Jurassic formations. In addition, the variation trends of 3He/4He ratio and δ13C1 value indicates that natural gas migration is from the Xujiahe formation to the Jurassic layer in the study area.

关键词： Western Sichuan Depression noble gas He and Ar isotopes natural gas migration

On Positively Complete Einstein Square Metrics

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Acta Mathematica Sinica,English Series 2023年

作者： zhongmin shen Hongmei ZHU College of Mathematics and Information Science Henan Normal University Department of Mathematical Sciences Indiana University-Purdue University

The well-known Berwald square metric is a positively complete and projectively flat Finsler metric with vanishing flag curvature. In this paper, we study a positively complete square metric on a manifold. We show a rigidity result that if the Ricci curvature is constant, then it must be isometric to the Berwald square metric. This is not true without assumption on the completeness of the metric.

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Riemann-Finsler Geometry with Applications to Information Geometry

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Chinese Annals of Mathematics,Series B 2006年第1期27卷 73-94页

作者： zhongmin shen Dedicated to the memory of Shiing-shen Chern

信息几何学是在数学的一个新分支，从微分几何学的应用发源到统计。在这篇论文我们简短 introduceRiemann-Finsler 几何学，我们在一个宽广得多的底上由建立信息几何学，以便信息几何学的潜在的应用将在统计以外。

关键词： Riemann-Finsler几何学信息几何学分支微分几何

On the projective Ricci curvature

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Science China Mathematics 2021年第7期64卷 1629-1636页

作者： zhongmin shen Liling Sun Department of Mathematical Sciences Indiana University-Purdue University IndianapolisIndianapolisIN 46202USA Department of Mathematics Taiyuan University of TechnologyTaiyuan 030024China School of Science Jimei UniversityXiamen 361021China

The notion of the Ricci curvature is defined for sprays on a manifold.With a volume form on a manifold,every spray can be deformed to a projective spray.The Ricci curvature of a projective spray is called the projective Ricci curvature.In this paper,we introduce the notion of projectively Ricci-flat sprays.We establish a global rigidity result for projectively Ricci-flat sprays with nonnegative Ricci curvature.Then we study and characterize projectively Ricci-flat Randers metrics.

关键词： spray Finsler metric Randers metric projective Ricci curvature

On a class of two-dimensional Finsler manifolds of isotropic S-curvature

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Science China Mathematics 2018年第1期61卷 57-72页

作者： Xinyue Cheng zhongmin shen Guojun Yang School of Mathematics and Statistics Chongqing University of Technology Department of Mathematical Sciences Indiana University-Purdue University Department of Mathematics Sichuan University

For an(α, β)-metric(non-Randers type) of isotropic S-curvature on an n-dimensional manifold with non-constant norm ‖β‖α, we first show that n = 2, and then we characterize such a class of two-dimensional(α, β)... 详细信息

关键词： (α,β)-metric Randers metric S-curvature

Curvature, Diameter and Bounded Betti Numbers

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Chinese Annals of Mathematics,Series B 2006年第2期27卷 143-152页

作者： Jyh-Yang WU Dedicated to the memory of Shiing-shen Chern

在这篇论文，我们介绍围住的 Betti 数字的观点，并且证明围住的 Betti 关上的 Riemannian 数 n 歧管(M， g ) 与 Ric (M) ≥ -(n - 1 ) 并且 Diam (M) ≤ D 被取决于 D 和 n 的一个数字围住。我们也证明有 onlyfinitely，许多等轴的同... 详细信息

在这篇论文，我们介绍围住的 Betti 数字的观点，并且证明围住的 Betti 关上的 Riemannian 数 n 歧管(M， g ) 与 Ric (M) ≥ -(n - 1 ) 并且 Diam (M) ≤ D 被取决于 D 和 n 的一个数字围住。我们也证明有 onlyfinitely，许多等轴的同晶型围住的 cohomology 组打字(H~*(M) ，在关上的 Riemannian 之中的‖·‖ _ ∞) 歧管(M， g ) 与 K (M) ≥ -1 和 Diam (M) ≤ D。

关键词：直径 Ricci曲率可组合曲率有界上同调有界Betti数