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	1. Invariants of Time-like Curves in Lorentzian Spacetime
	Wei LI
	Mathematics 26 February 2014
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	Abstract:This paper derives a family of invariants for time-like curves directly from the equation of its moving frames in Lorentzian spacetime. By the invariants this paper studies some geometric aspects of time-like curves in Lorentzian spacetime. In order to illustrate the necessity of constructing these invariants, this paper firstly reviews the traditional method with Frenet frame. Then one easily gets to find that for extending scope of application, it is necessary to discuss how to describe geometrical properties of curves with general orthonormal frames. A natural idea is to construct a family of invariants corresponding to orthonormal frames. These new invariants not only extend the traditional ones corresponding to Frenet frames, but also have better operability.
	TO cite this article:Wei LI . Invariants of Time-like Curves in Lorentzian Spacetime[OL].[26 February 2014] http://en.paper.edu.cn/en_releasepaper/content/4587044


	2. $5$-dimensional constant Gauss-Kroneckercurvature hypersurfaces of spheres
	Perdomo Oscar,Wei Guoxin
	Mathematics 12 February 2014
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	Abstract:Let $Msubset S^{6}$ be a complete orientable hypersurface with constant Gauss-Kronecker curvature $G$. For any $vin R^{7}$, let us define the following two real functions $l_v, f_v:M o R$on $M$ by $l_v(x)=<x,v>$ and $f_v(x)=<u(x),v>$ with $u:M o S^{6}$ a Gauss map of $M$. We show that if $l_v=lambda f_v$ for some nonzero vector $vin R^{7}$ and some real number $lambda$ and $(lambda^2-1)^2+(G^2-1)^2eq 0$, then $M$ is either $S^5(r)$ or $M$ is $S^k(r) imes S^{5-k}(sqrt{1-r^2})$.
	TO cite this article:Perdomo Oscar,Wei Guoxin. $5$-dimensional constant Gauss-Kroneckercurvature hypersurfaces of spheres[OL].[12 February 2014] http://en.paper.edu.cn/en_releasepaper/content/4585284

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	3. Two interesting examples
	Perdomo Oscar, Wei Guoxin
	Mathematics 11 February 2014
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	Abstract:Firstly, we will show with an example that the completeness condition is needed in our result. Secondly, we will give an example of a complete hypersurface in $S^5$ with constant Gauss-Kronecker curvature that satisfies the condition $l_v=lambda f_v$ for some non zero $v$, which is neither a totally umbilical hypersurface nor a cartesian product of Euclidean spheres.
	TO cite this article:Perdomo Oscar, Wei Guoxin. Two interesting examples[OL].[11 February 2014] http://en.paper.edu.cn/en_releasepaper/content/4585082


	4. MEAN CURVATURE TYPE FLOW WITH PERPENDICULAR NEUMANN BOUNDARY CONDITION INSIDE A CONVEX CONE
	Guo Fangcheng,LI Guanghan,WU Chuanxi
	Mathematics 21 January 2014
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	Abstract:In this paper, we investigate the evolution of hypersurfaces with perpendicular Neumann boundary condition under mean curvature type flow, where the boundary manifold is a convex cone. We find that the volume surrounded by the cone and the evolving hypersurface is invariant. By maximal principle we prove that the solutions of this flow exist for all time and converge to some part of a sphere exponentially as time tends to infinity.
	TO cite this article:Guo Fangcheng,LI Guanghan,WU Chuanxi. MEAN CURVATURE TYPE FLOW WITH PERPENDICULAR NEUMANN BOUNDARY CONDITION INSIDE A CONVEX CONE[OL].[21 January 2014] http://en.paper.edu.cn/en_releasepaper/content/4583356


	5. DIFFEOMORPHIC THEOREMS FOR OPEN RIEMANNIAN MANIFOLDS WITH RADIAL CURVATURE BOUNDED BELOW
	XIE Zhiqi,LI Guanghan,WU Chuanxi
	Mathematics 14 January 2014
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	Abstract:In this paper, we study complete non-compact Riemannian manifolds with radial curvature bounded from below by that of a non-compact model surface of revolution. We find a reasonable condition to ensure that this kind of manifolds is diffeomorphic to a Euclidean space if it contains enough rays starting from a base point.
	TO cite this article:XIE Zhiqi,LI Guanghan,WU Chuanxi. DIFFEOMORPHIC THEOREMS FOR OPEN RIEMANNIAN MANIFOLDS WITH RADIAL CURVATURE BOUNDED BELOW[OL].[14 January 2014] http://en.paper.edu.cn/en_releasepaper/content/4581995


	6. Hypersurfaces with Prescribed $lpha$-Relative Gauss-Kronecker Curvature
	WU Yadong,ZHAO Guosong
	Mathematics 25 December 2013
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	Abstract:Considering the $lpha$-relative normalizationon hypersurfaces, we derive the equations of hypersurfaces with$lpha$-relative Gauss-Kronecker curvature. By solving two linkedMonge-Amp$grave{e}$re equations with Dirichlet boundary conditions,we construct hyperbolic hypersurfaces such that their$lpha$-relative Gauss-Kronecker curvature are the given functions.
	TO cite this article:WU Yadong,ZHAO Guosong. Hypersurfaces with Prescribed $lpha$-Relative Gauss-Kronecker Curvature[OL].[25 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4578330


	7. Existence of homogeneous geodesics on homogeneous Randers spaces
	Yan Zaili, Deng Shaoqiang
	Mathematics 23 December 2013
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	Abstract:A geodesic of a Finsler space $(M, F)$ is called homogeneous if it is the orbit of a one-parameter transformation group of isometries of $(M, F)$. In this paper we show that every homogeneous Randers space admits at least a homogeneous geodesic through any point.
	TO cite this article:Yan Zaili, Deng Shaoqiang. Existence of homogeneous geodesics on homogeneous Randers spaces[OL].[23 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4577145


	8. Finsler spaces whose geodesics are orbits
	Yan Zaili, Deng Shaoqiang
	Mathematics 20 December 2013
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	Abstract:n this paper, we study Finsler spaces whose geodesics are the orbits of one-parameter subgroups of the group of isometries (abbreviated as Finsler g.o. spaces). We first generalize some geometric results on Riemannian g.o. spaces to the Finslerian setting. Then we show that a Finsler g.o. nilmanifold is at most two step nilpotent and construct some examples of g.o. spaces which are neither Berwaldian nor weakly symmetric. Further, we give a sufficient and necessary condition for a Randers space to be a g.o. space.
	TO cite this article:Yan Zaili, Deng Shaoqiang. Finsler spaces whose geodesics are orbits[OL].[20 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4577148


	9. Equigeodesics on Generalized Flag Manifolds with $b_2(G/K)=1$
	WANG Yu, ZHAO Guo-Song
	Mathematics 17 December 2013
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	Abstract:In this paper we provide a characterization of structural equigeodesics on generalized flag manifolds with second Betti number $b_2(G/K)=1$, and give examples of structural equigeodesics on generalized flag manifolds of the exceptional Lie groups $F_4, E_6$ and $E_7$ with three isotropy summands.
	TO cite this article:WANG Yu, ZHAO Guo-Song. Equigeodesics on Generalized Flag Manifolds with $b_2(G/K)=1$[OL].[17 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4575924


	10. $L^{2}$-eta form for locally compact group action
	SU GuangXiang
	Mathematics 11 December 2013
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	Abstract:Eta invariant is a very important invariant in global analysis on manifolds. Eta-invariant was defined by Atiyah-Patodi-Singer. Since then, people had done many studies and extensions of it. In this paper, for a locally compact unimodular group acting on a fiber bundle, under some conditions we define eta form on it.
	TO cite this article:SU GuangXiang. $L^{2}$-eta form for locally compact group action[OL].[11 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4574213

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