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41.
In a given Kähler manifold (M,J) we introduce the notion of Kähler Frenet curves, which is closely related to the complex structure J of M. Using the notion of such curves, we characterize totally geodesic Kähler immersions of M into an ambient Kähler manifold and totally geodesic immersions of M into an ambient real space form of constant sectional curvature . 相似文献
42.
对于图G(或有向图D)内的任意两点u和v,u—v测地线是指在u和v之间(或从u到v)的最短路.I(u,v)表示位于u—v测地线上所有点的集合,对于S(?)V(G)(或V(D)),I(S)表示所有I(u,v)的并,这里u,v∈S.G(或D)的测地数g(G)(或g(D))是使I(S)=V(G)(或I(S)=V(D))的点集S的最小基数.G的下测地数g~-(G)=min{g(D):D是G的定向图},G的上测地数g~ (G)=max{g(D):D是G的定向图}.对于u∈V(G)和v∈V(H),G_u H_v表示在u和v之间加一条边所得的图.本文主要研究图G_u H_v的测地数和上(下)测地数. 相似文献
43.
《复变函数与椭圆型方程》2012,57(12):1071-1075
We show in this article that there exists conjugate points at infinity in infinite dimensional Teichmüller spaces. 相似文献
44.
Sergio Benenti 《Acta Appl Math》2005,87(1-3):33-91
A general analysis of special classes of symmetric two-tensor on Riemannian manifolds is provided. These tensors arise in connection with special topics in differential geometry and analytical mechanics: geodesic equivalence and separation of variables. It is shown that they play an important role in the theory of correspondent (or equivalent) dynamical systems of Levi-Civita. By applying some new developments of this theory, it is shown that the recent notions of cofactor and cofactor-pair systems arise in a natural way, as non-Lagrangian systems having a Lagrangian equivalent. This circumstance extends the Hamiltonian methods, including the separation of variables of the Hamilton–Jacobi equation, to a special class of nonconservative systems. In this extension the case of indefinite metrics, may occur. Hence, it is shown that also pseudo-Riemannian geometry plays an important role also in classical mechanics.Research sponsored by the Dept. of Mathematics, University of Turin, and by INDAM-GNFM. 相似文献
45.
J. Carlos Díaz-Ramos Eduardo García-Río Luis Hervella 《Annali di Matematica Pura ed Applicata》2005,184(1):115-130
Total scalar curvatures of geodesic spheres obtained by integrating the second-order scalar invariants of the curvature tensor are investigated. The first terms in their power-series expansions are derived and these results are used to characterize the two-point homogeneous spaces among Riemannian manifolds with adapted holonomy. Dedicated to Professor L. VanheckeMathematics Subject Classification (2000) 53C25, 53C30 相似文献
46.
Segmentation under geometrical conditions using geodesic active contours and interpolation using level set methods 总被引:3,自引:0,他引:3
Let I: be a given bounded image function, where is an open and bounded domain which belongs to n. Let us consider n=2 for the purpose of illustration. Also, let S={xi}i be a finite set of given points. We would like to find a contour , such that is an object boundary interpolating the points from S. We combine the ideas of the geodesic active contour (cf. Caselles et al. [7,8]) and of interpolation of points (cf. Zhao et al. [40]) in a level set approach developed by Osher and Sethian [33]. We present modelling of the proposed method, both theoretical results (viscosity solution) and numerical results are given.
AMS subject classification 49L25, 74G65, 68U10 相似文献
47.
本文研究了保持Ricci曲率不变的Finsler射影变换。给定一个紧致无边的n维可微流形M,证明了:对于一个从M上的Berwald度量到Riemann度量的C-射影变换,如果Berwald度量的Ricci曲率关于Riemann度量的迹不超过Riemann度量的标量曲率,则该射影变换是平凡的。 相似文献
48.
局部对称黎曼流形中的极小子流形 总被引:1,自引:0,他引:1
In this paper, we discuss the compact minimal submanifolds in locally symmetric Riemannian manifolds. Two Pinching theorems are obtained and two corresponding results of Chern, S. S. and Yau S. T. are generalized. 相似文献
49.
本文我们得到了$(\alpha,\beta)$-度量的测地系数$G^{i}(x,y)$和其逆$G^{i}(x,-y)$有相同Douglas曲率的充分必要条件.这个充分必要条件恰好是$(\alpha,\beta)$-度量具有可反测地线的充分必要条件. 相似文献
50.
Motivated by Bonahon’s result for hyperbolic surfaces, we construct an analogue of the Patterson–Sullivan–Bowen–Margulis map
from the Culler–Vogtmann outer space CV (F
k
) into the space of projectivized geodesic currents on a free group. We prove that this map is a continuous embedding and
thus obtain a new compactification of the outer space. We also prove that for every k ≥ 2 the minimum of the volume entropy of the universal covers of finite connected volume-one metric graphs with fundamental
group of rank k and without degree-one vertices is equal to (3k − 3) log 2 and that this minimum is realized by trivalent graphs with all edges of equal lengths, and only by such graphs.
Received: December 2005, Accepted: March 2006 相似文献