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71.
Bang-Yen Chen 《Central European Journal of Mathematics》2009,7(3):400-428
Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as
well as in physics. Spatial surfaces in 4D Lorentzian space forms with parallel mean curvature vector were classified by B.
Y. Chen and J. Van der Veken in [9]. Recently, spatial surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean
spaces are also classified in [7]. In this article, we classify spatial surfaces with parallel mean curvature vector in pseudo-Riemannian
spheres and pseudo-hyperbolic spaces with arbitrary codimension and arbitrary index. Consequently, we achieve the complete
classification of spatial surfaces with parallel mean curvature vector in all pseudo-Riemannian space forms. As an immediate
by-product, we obtain the complete classifications of spatial surfaces with parallel mean curvature vector in arbitrary Lorentzian
space forms.
相似文献
72.
In crystal optics and quantum electrodynamics in gravitational vacua, the propagation of light is not described by a metric, but an area metric geometry. In this article, this prompts us to study conditions for linear electrodynamics on area metric manifolds to be well-posed. This includes an identification of the timelike future cones and their duals associated to an area metric geometry, and thus paves the ground for a discussion of the related local and global causal structures in standard fashion. In order to provide simple algebraic criteria for an area metric manifold to present a consistent spacetime structure, we develop a complete algebraic classification of area metric tensors up to general transformations of frame. This classification, valuable in its own right, is then employed to prove a theorem excluding the majority of algebraic classes of area metrics as viable spacetimes. Physically, these results classify and drastically restrict the viable constitutive tensors of non-dissipative linear optical media. 相似文献
73.
74.
75.
Let s : S2 → G(2, 5) be a linearly full totally unramified pseudo-holomorphic curve with constant Gaussian curvature K in a complex Grassmann manifold G(2, 5). It is prove that K is either 1 4 1 or 4/5 if s is non-±holomorphic. Furthermore, K = 1/3 if and only if s is totally real. We also prove that the Gaussian curvature K is either 1 or -4/3 if s is a non-degenerate holomorphic curve under some conditions. 相似文献
76.
Maria Fernanda Elbert 《Proceedings of the American Mathematical Society》2000,128(5):1443-1450
We generalize Efimov's Theorem for graphs in Euclidean space using the scalar curvature, with an additional hypothesis on the second fundamental form. 相似文献
77.
P. Anselmo-Filho S. Hochgreb R.S. Barlow R.S. Cant 《Proceedings of the Combustion Institute》2009,32(2):1763-1770
Combustion under stratified conditions is common in many systems. However, relatively little is known about the structure and dynamics of turbulent stratified flames. Two-dimensional imaging diagnostics are applied to premixed and stratified V-flames at a mean equivalence ratio of 0.77, and low turbulent intensity, within the corrugated flame range. The present results show that stratification affects the mean turbulent flame speed, structure and geometric properties. Stratification increases the flame surface density above the premixed flame levels in all cases, with a maximum reached at intermediate levels of stratification. The flame surface density (FSD) of stratified flames is higher than that of premixed flames at the same mean equivalence ratio. Under the present conditions, the FSD peaks at a stratification ratio around 3.0. The FSD curves for stratified flames are further skewed towards the product side. The distribution of flame curvature in stratified flames is broader and more symmetric relative to premixed flames, indicating an additional mechanism of curvature generation, which is not necessarily due to cusping. These experiments indicate that flame stratification affects the intrinsic behaviour of turbulent flames and suggest that models may need to be revised in the light of the current evidence. 相似文献
78.
79.
Igor Leite Freire 《Journal of Mathematical Analysis and Applications》2010,367(2):716-9473
Using the scalar curvature of the product manifold S2×R and the complete group classification of nonlinear Poisson equation on (pseudo) Riemannian manifolds, we extend the previous results on symmetry analysis of homogeneous wave equation obtained by H. Azad and M.T. Mustafa [H. Azad, M.T. Mustafa, Symmetry analysis of wave equation on sphere, J. Math. Anal. Appl. 333 (2007) 1180-1188] to nonlinear Klein-Gordon equations on the two-dimensional sphere. 相似文献
80.
Eva Tourís 《Journal of Mathematical Analysis and Applications》2011,380(2):865-881
In this paper we obtain the equivalence of the Gromov hyperbolicity between an extensive class of complete Riemannian surfaces with pinched negative curvature and certain kind of simple graphs, whose edges have length 1, constructed following an easy triangular design of geodesics in the surface. 相似文献