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On Nonuniqueness of geodesics and Geodesic Disks in the Universal Asymptotic Teichmüller Space

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Acta Mathematica Sinica,English Series 2017年第2期33卷 201-209页

作者： Yi QI Yan WU LMIB and School of Mathematics and Systems Science Beihang University Beijing 100191 P. R. China School of Science Linyi University Linyi 276005 P. R. China

Abstract The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmfiller space AT（D） are studied in this paper. It is proved that if # is asymptotically extremal in [[#]] with h （μ）〈 h＊（μ） for some point ζ∈D, then there exist infinitely many geodesic segments joining [[0]] and [[μ]], and infinitely many holomorphic geodesic disks containing [[0]] and [μ]] in AT（D）.

关键词： Asymptotic Teichmuller space geodesics geodesic disks holomorphic isometry Teichmul-ler metric

Morse index and the stability of closed geodesics

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Science China Mathematics 2010年第5期53卷 170-175页

作者： Hu XiJun Sun ShanZhong Shandong Univ Sch Math Jinan 250100 Peoples R China Capital Normal Univ Sch Math Sci Beijing 100048 Peoples R China

Let ind(c) be the Morse index of a closed geodesic c in an(n+1)-dimensional Riemannian manifold M.We prove that an oriented closed geodesic c is unstable if n + ind(c) is odd and a non-oriented closed geodesic c is unstable if n + ind(c) is even.Our result is a generalization of the famous theorem due to Poincar'e which states that the closed minimizing geodesic on a Riemann surface is unstable.

关键词： closed geodesics stability Morse index

Some Remarks on the geodesics in Infinite Dimensional Teichmuller Spaces

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Acta Mathematica Sinica,English Series 1997年第4期13卷 497-502页

作者： Shen Yuliang Department of Mathematics, Suzhou University, Suzhou 215006, China 苏州大学数学系江苏苏州

Let B denote the set of those points p in an infinite dimensional Teichmiiller space such that a geodesic between the zero point and p is not unique. Some properties of the set B are given.

关键词： Quasiconformal mappings Teichmuller spaces Extremal quasiconformal Beltramis geodesics

The properties and geodesics related to the NUT-Taub-like spacetime

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Chinese Physics B 2006年第5期15卷 927-933页

作者：吴亚波赵国明邓雪梅杨秀一吕剑波李松 Department of Physics Liaoning Normal University Dalian 116029 China

Some properties related to the NUT-Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT-Taub-like black hole are discussed. Furthermore, the geodesics in the NUT-Taub-like spacetime are obtained in some special cases. Specifically, the circular orbits for a massive particle are derived, which can reduce to the cases of the Schwarzschild spacetime and the NUT-Taub spacetime when m^＊ = 0 and m^＊〈〈 M, respectively.

关键词： NUT-Taub spacetime Schwarzschild metric geodesics

Schwarzschild geodesics in Terms of Elliptic Functions and the Related Red Shift

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Journal of Modern Physics 2011年第4期2卷 274-283页

作者： Gunter Scharf 不详

Using Weierstrassian elliptic functions the exact geodesics in the Schwarzschild metric are expressed in a simple and most transparent form. The results are useful for analytical and numerical applications. For example we calculate the perihelion precession and the light deflection in the post-Einsteinian approximation. The bounded orbits are computed in the post-Newtonian order. As a topical application we calculate the gravitational red shift for a star moving in the Schwarzschild field.

关键词： Schwarzschild geodesics Red Shift

Closed　geodesics　and　Non一Differentiability　of　the　Metric　in　Infinite－Dimensional　Teichmuller　Spaces

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数学进展 1995年第1期 81-83页

作者：李忠

ＣｌｏｓｅｄＧｅｏｄｅｓｉｃｓａｎｄＮｏｎ一ＤｉｆｆｅｒｅｎｔｉａｂｉｌｉｔｙｏｆｔｈｅＭｅｔｒｉｃｉｎＩｎｆｉｎｉｔｅ－ＤｉｍｅｎｓｉｏｎａｌＴｅｉｃｈｍｕｌｌｅｒＳｐａｃｅｓＬｉｚｈｏｎｇ（李忠）（Ｄｅｐａｒｔｍ... 详细信息

ＣｌｏｓｅｄＧｅｏｄｅｓｉｃｓａｎｄＮｏｎ一ＤｉｆｆｅｒｅｎｔｉａｂｉｌｉｔｙｏｆｔｈｅＭｅｔｒｉｃｉｎＩｎｆｉｎｉｔｅ－ＤｉｍｅｎｓｉｏｎａｌＴｅｉｃｈｍｕｌｌｅｒＳｐａｃｅｓＬｉｚｈｏｎｇ（李忠）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，...

关键词：李忠 Dimensional Teichmuller geodesics and Metric the Closed Differentiability

Characterization of Gromov Hyperbolic Short Graphs

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Acta Mathematica Sinica,English Series 2014年第2期30卷 197-212页

作者： José Manuel RODRIGUEZ Departamento de Matemticas Universidad Carlos III de MadridAvenida de la Universidad 30

To decide when a graph is Gromov hyperbolic is,in general,a very hard problem.In this paper,we solve this problem for the set of short graphs（in an informal way,a graph G is r-short if the shortcuts in the cycles of G have length less than r）：an r-short graph G is hyperbolic if and only if S9r（G）is finite,where SR（G）：=sup{L（C）：C is an R-isometric cycle in G}and we say that a cycle C is R-isometric if dC（x,y）≤dG（x,y）＋R for every x,y∈C.

关键词： Short graph Gromov hyperbolicity Gromov hyperbolic graph infinite graphs geodesics

A dynamical approach to the exterior geometry of a perfect fluid as a relativistic star

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Chinese Physics C 2013年第2期37卷 26-38页

作者： Mohsen Fathi Department of Physics Islamic Azad University Central Tehran Branch Tehran Iran

In this article, we assume that a cold charged perfect fluid is constructing a spherical relativistic star. Our purpose is the investigation of the dynamical properties of its exterior geometry, through simulating the... 详细信息

关键词： astrophysics relativistic stars geodesics

Misconceptions of Universe Expansion, Accelerated Universe Expansion, and Their Sources. Virtual Reality of Inflationary Cosmology

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Journal of Modern Physics 2018年第6期9卷 1326-1359页

作者： Georg von Brzeski Vadim von Brzeski Helios Labs 945 Hoxett St. Gilroy CA 95020 USA

In this work, we present our theory and principles of the mathematical foundations of Lobachevskian (hyperbolic) astrophysics and cosmology which follow from a mathematical interpretation of experimental data in a Lobachevskian non-expanding Universe. Several new scientific formulas of practical significance for astrophysics, astronomy, and cosmology are presented. A new method of calculating (from experimental data) the curvature of a Lobachevskian Universe is given, resulting in an estimated curvature-K on the order of 10−52 m−2. Our model also estimates the radius of the non-expanding Lobachevskian Universe in a Poincare ball model as approximately 14.9 bly. A rigorous theoretical explanation in terms of the fixed Lobachevskian geometry of a non-expanding Universe is provided for experimental data acquired in the Supernova Project, showing an excellent agreement between experimental data and our theoretical formulas. We present new geometric equations relating brightness dimming and redshift, and employ them to fully explain the erroneous reasoning and erroneous conclusions of Perlmutter, Schmidt, Riess and the 2011 Nobel Prize Committee regarding “accelerated expansion” of the Universe. We demonstrate that experimental data acquired in deep space astrophysics when interpreted in terms of Euclidean geometry will result in illusions of space expansion: an illusion of “linear space expansion”—Hubble, and an illusion of “accelerated (non-linear) space expansion”—Perlmutter, Schmidt, Riess.

关键词： Non-Expanding Universe Hyperbolic Universe Supernova Photometry 2011 Nobel Physics Prize Lobachevskian Geometry Geometry of geodesics