共查询到19条相似文献,搜索用时 125 毫秒
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文章研究了三角范畴D及其coherent函子范畴A(D)的recollement之间的关系.利用D的recollement可以诱导A(D)的prerecollement,文章证明了该prerecollement是recollement的充分必要条件是D的recollement是可裂的;并且D的recollement可以诱导A(D)的prerecollement. 相似文献
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本文研究了容有半对称度量联络的广义复空间中的子流形上的Chen-Ricci不等式.利用代数技巧,建立了子流形上的Chen-Ricci不等式.这些不等式给出了子流形的外在几何量-关于半对称联络的平均曲率与内在几何量-Ricci曲率及k-Ricci曲率之间的关系,推广了Mihai和Özgür的一些结果. 相似文献
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利用Chern联络D、Cartan张量A以及第二基本形式H.研究了Finsler子流形中的诱导Chern联络与第一、第二曲率R和P,给出了子流形的关于R曲率、P曲率以及flag曲率的Gauss方程。 相似文献
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本文研究了D4 型量子包络代数的Gelfand-Kirillov 维数的计算问题. 利用文献[1] 中给出的Gelfand-Kirillov 维数的计算方法和文献[2] 中给出的D4 型量子包络代数的Groebner-Shirshov 基计算了D4型量子包络代数的Gelfand-Kirillov 维数, 得到的主要结果是D4 型量子包络代数的Gelfand-Kirillov 维数为28. 希望此结果为计算Dn型量子包络代数的Gelfand-Kirillov 维数提供一些思路. 相似文献
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设M为n维复流形,F为M上的强拟凸的复Finsler度量,M是M的m维复子流形,F是F在M上诱导的复Finsler度量,D为(M,F)上的复Rund联络.本文证明了(1)(M,F)上的诱导复线性联络△↓的全纯曲率与(M,F)上的复Rund联络△↓^*的全纯曲率相同;(2)联络△↓^*的全纯曲率不超过联络D的全纯曲率;(3)(M,F)是(M,F)的全测地复Finsler子流形的充分必要条件是(M,F)的第2基本形式B(.,.)的适当形式的缩并为零,即B(x,l)=0.本文的证明主要利用复Finsler子流形(M,F)的Gauss,Codazzi和Ricci方程. 相似文献
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ON THE CHERN CONNECTION OF FINSLER SUBMANIFOLDS 总被引:2,自引:0,他引:2
This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric.Then the authors point out a difference between Finsler submanifolds and Riemann submanifolds. 相似文献
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《Nonlinear Analysis: Real World Applications》2007,8(4):1132-1143
In [G. Munteanu, Complex Spaces in Finsler, Lagrange and Hamilton Geometries, vol. 141, Kluwer Academic Publishers, Dordrecht, FTPH, 2004.] we underlined the motifs of a remarkable class of complex Finsler subspaces, namely the holomorphic subspaces. With respect to the Chern–Finsler complex connection (see [M. Abate, G. Patrizio, Finsler Metrics—A Global Approach, Lecture Notes in Mathematics, vol. 1591, Springer, Berlin, 1994.]) we studied in [G. Munteanu, The equations of a holomorphic subspace in a complex Finsler space, Publicationes Math. Debrecen, submitted for publication.] the Gauss, Codazzi and Ricci equations of a holomorphic subspace, the aim being to determine the interrelation between the holomorphic sectional curvature of the Chern–Finsler connection and that of its induced tangent connection.In the present paper, by means of the complex Berwald connection, we study totally geodesic holomorphic subspaces. With respect to complex Berwald connection the equations of the holomorphic subspace have simplified expressions. The totally geodesic subspace request is characterized by using the second fundamental form of complex Berwald connection. 相似文献
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In this paper, the Laplacian on the holomorphic tangent bundle T1,0M of
a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric
is defined and its explicit expression is obtained by using the Chern Finsler connection
associated with (M,F). Utilizing the initiated “Bochner technique”, a vanishing theorem
for vector fields on the holomorphic tangent bundle T1,0M is obtained. 相似文献
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Sofiane Bouarroudj 《Indagationes Mathematicae》2004,15(3):321-338
Let (M, F) be a Finsler manifold. We construct a 1-cocycle on Diff(M) with values in the space of differential operators acting on sections of some bundles, by means of the Finsler fonction F. As an operator, it has several expressions: in terms of the Chern, Berwald, Cartan or Hashiguchi connection, although its cohomology class does not depend on them. This cocycle is closely related to the conformal Schwarzian derivatives introduced in our previous work. The second main result of this paper is to discuss some properties of the conformally invariant quantization map by means of a Sazaki (type) metric on the slit bundle T Minduced by F. 相似文献
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Motivated by some issues which enter into the Gauss-Bonnet-Chern theorem in Finsler geometry, this paper studies the unit tangent sphere (or indicatrix) Ix M at each point x of a Pinsler manifold M. We demonstrate that the volume of ImM, calculated with respect to a Riemannian metric induced naturally by the Finsler structure, is in general a function of x. This contrasts sharply with the situation in Riemannian geometry. We also express the derivative of such volume function in terms of the second curvature tensor of the Chern connection. In particular, we find that this function is constant on Landsberg spaces (though that constant need not be equal to the value taken by Riemannian manifolds). 相似文献
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Gheorghe Munteanu 《Periodica Mathematica Hungarica》2007,55(1):97-112
In [Mu1] we underlined the motifs of holomorphic subspaces in a complex Finsler space: induced nonlinear connection, coupling
connections, and the induced tangent and normal connections. In the present paper we investigate the equations of Gauss, H-and A-Codazzi, and Ricci equations of a holomorphic subspace. We deduce the link between the holomorphic curvatures of the Chern-Finsler
connection and its induced tangent connection. Conditions for totally geodesic holomorphic subspaces are obtained.
Communicated by János Szenthe 相似文献
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In this note we discuss a few properties of transnormal Finsler functions, i.e., the natural generalization of distance functions and isoparametric Finsler functions. In particular, we prove that critical level sets of an analytic transnormal function are submanifolds, and the partition of M into level sets is a Finsler partition, when the function is defined on a compact analytic manifold M. 相似文献
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The term integral geometry has come to describe two different fields of research: one, geometrical, based on the works of Blaschke, Chern, and Santaló,
and another, analytical, based on the works of Radon, John, Helgason, and Gelfand. In this paper we bridge the gap by showing
that classical integral-geometric formulas such as those of Crofton, Cauchy, and Chern can be easily and systematically obtained
through the study of Radon-type transforms on double fibrations. The methods also allow us to extend these formulas to non-homogeneous
settings where group-theoretic techniques are no longer useful. To illustrate this point, we construct all Finsler metrics
on projective space such that hyperplanes are area-minimizing and extend the theory of Crofton densities developed by Busemann,
Pogorelov, Gelfand, and Smirnov.
Pensar es olvidar diferencias. . . Jorge Luis Borges相似文献
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The term integral geometry has come to describe two different fields of research: one, geometrical, based on the works of Blaschke, Chern, and Santaló,
and another, analytical, based on the works of Radon, John, Helgason, and Gelfand. In this paper we bridge the gap by showing
that classical integral-geometric formulas such as those of Crofton, Cauchy, and Chern can be easily and systematically obtained
through the study of Radon-type transforms on double fibrations. The methods also allow us to extend these formulas to non-homogeneous
settings where group-theoretic techniques are no longer useful. To illustrate this point, we construct all Finsler metrics
on projective space such that hyperplanes are area-minimizing and extend the theory of Crofton densities developed by Busemann,
Pogorelov, Gelfand, and Smirnov.
Pensar es olvidar diferencias. . . Jorge Luis Borges相似文献