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101.
Using the convex functions on Grassmannian manifolds, the authors obtain the interior estimates for the mean curvature flow of higher codimension. Confinable properties of Gauss images under the mean curvature flow have been obtained, which reveal that if the Gauss image of the initial submanifold is contained in a certain sublevel set of the v-function, then all the Gauss images of the submanifolds under the mean curvature flow are also contained in the same sublevel set of the v-function. Under such restrictions, curvature estimates in terms of v-function composed with the Gauss map can be carried out. 相似文献
102.
Under the hypothesis of mean curvature flows of hypersurfaces, we prove that the limit of the smooth rescaling of the singularity is weakly convex. It is a generalization of the result due to G.Huisken and C. Sinestrari in. These apriori bounds are satisfied for mean convex hypersurfaces in locally symmetric Riemannian manifolds with nonnegative sectional curvature. 相似文献
103.
104.
The purpose of this note is to exhibit some simple and basic constructions for smooth compact transformation groups, and some of their most immediate applications to geometry. 相似文献
105.
We prove the existence of a geometric characteristic submanifold for non-positively curved manifolds of any dimension greater
than or equal to three. In dimension three, our result is a geometric version of the topological characteristic submanifold
theorem due to Jaco, Shalen and Johannson.
Received: May 20, 1996 相似文献
106.
The authors show that the 2-non-negative traceless bisectional curvature is preserved along the K(a)hler-Ricci flow.The positivity of Ricci curvature is also preserved along the K(a)hler-Ricci flow with 2-non-negative traceless bisectional curvature.As a corollary,the K(a)hler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a K(a)hler-Ricci soliton in the sense of Cheeger-Gromov-Hausdorff topology if complex dimension n≥3. 相似文献
107.
We study projective curvature tensor in K-contact and Sasakian manifolds. We prove that (1) if a K-contact manifold is quasi projectively flat then it is Einstein and (2) a K-contact manifold is ξ-projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a K-contact manifold to be quasi projectively flat and φ-projectively flat are obtained. We also prove that for a (2n + 1)-dimensional Sasakian manifold the conditions of being quasi projectively flat, φ-projectively flat and locally isometric to the unit sphere S
2n+1 (1) are equivalent. Finally, we prove that a compact φ-projectively flat K-contact manifold with regular contact vector field is a principal S
1-bundle over an almost Kaehler space of constant holomorphic sectional curvature 4. 相似文献
108.
In this article, we obtain some results about the mean curvature integrals of the parallel body of a convex set in R^n. These mean curvature integrals are generalizations of the Santalo's results. 相似文献
109.
A multidimensional advection scheme in 3D based on the use of face‐matched flux polyhedra to integrate the volume fraction evolution equation is proposed. The algorithm tends to reduce the formation of ‘over/undershoots’ by alleviating the over/underlapping of flux polyhedra, thus diminishing the need to use local redistribution algorithms. The accuracy and efficiency of the proposed advection algorithm, which are analyzed using different tests with prescribed velocity field, compare well with other multidimensional advection methods proposed recently. The algorithm is also applied, in combination with a Navier–Stokes solver, to reproduce the impact of a water droplet falling through air on a pool of deep water. The interfacial curvature is calculated using a height‐function technique with adaptive stencil adjustment, which provides improved accuracy in regions of low grid resolution. The comparison of the numerical results with experimental results shows a good degree of agreement. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
110.
We study the prolongation of semibasic projectable tangent valued k-forms on fibered manifolds with respect to a bundle functor F on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear r-th order connection on the base manifold, where r is the base order of F. We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and the tangent functor are discussed in detail. Next we clarify how this prolongation procedure can be extended to arbitrary projectable tangent valued k-forms in the case F is a fiber product preserving bundle functor on the category of fibered manifolds with m-dimensional bases and local diffeomorphisms as base maps. 相似文献