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 共查询到19条相似文献,搜索用时 62 毫秒
1.
Complex manifolds are topological spaces that are covered by coordinate charts where the coordinate changes are given by holomorphic transformations.For example,Riemann surfaces are one dimensional complex manifolds.In order to understand complex manifolds,it is useful to introduce metrics that are compatible with the complex structure.In general,we should have a pair(M,ds~2_M)where ds~2_M is the metric.The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries.Such metrics can naturally be used to describe invariants of the complex structures of the manifold.  相似文献   

2.
The author studies the regularity of energy minimizing maps from Finsler manifolds to Riemannian manifolds.It is also shown that the energy minimizing maps are smooth,when the target manifolds have no ...  相似文献   

3.
In the present paper, we construct two approximate inertial manifolds for the generalized symmetric regularized long wave equations with damping term. The orders of approximations of these manifolds to the global attractor are derived.  相似文献   

4.
In this article, we determine the multiple point set of immersions of 6-dimensional manifolds into 7-dimensional Euclidean space R7. The method is to evaluate the characteristic numbers of these manifolds. By a certain method, these numbers can be read of from the Hurewicz image ofh : π7QMO(1) → H7QMO(1).In particular, we show that for any immersion of P 6 in R7 the double, 4-fold and 6-fold point manifolds are cobordant to boundaries and triple point manifolds cobordant to P 4, 5-fold point manifolds cobordant to P 2 and 7-fold point manifold are odd number.  相似文献   

5.
The author obtains the theorems of Barth-Lefschetz type on Kahler manifolds with partially positive bisectional curvature without the assumption of nonnegative bisectional curvature. Some applications of the results to holomorphic mappings are given.  相似文献   

6.
The authors study the bifurcation of homoclinic orbits from a degenerate homoclinic orbit in reversible system. The unperturbed system is assumed to have saddle-center type equilibrium whose stable and unstable manifolds intersect in two-dimensional manifolds. A perturbation technique for the detection of symmetric and nonsymmetric homoctinic orbits near the primary homoclinic orbits is developed. Some known results are extended.  相似文献   

7.
In this article, we determine the multiple point set of immersions of 6-dimensional manifolds into 7-dimensional Euclidean space R7. The method is to evaluate the characteristic numbers of these manifolds. By a certain method, these numbers can be read of from the Hurewicz image ofh : π7QMO(1) → H7QMO(1).In particular, we show that for any immersion of P 6 in R7 the double, 4-fold and 6-fold point manifolds are cobordant to boundaries and triple point manifolds cobordant to P 4, 5-fold point manifolds cobor...  相似文献   

8.
任长宇  王光烈 《东北数学》2007,23(5):413-424
This paper deals with a class of parabolic Monge-Ampère equation on Riemannian manifolds. The existence and uniqueness of the solution to the first initial-boundary value problem for the equation are established.  相似文献   

9.
We discuss a class of complete Kaihler manifolds which are asymptotically complex hyperbolic near infinity. The main result is vanishing theorems for the second L2 cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincare inequality case and establish a vanishing theorem provided that the weighted function p is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighted Poincare inequality.  相似文献   

10.
We discuss a class of complete Khler manifolds which are asymptotically complex hyperbolic near infinity . The main result is vanishing theorems for the second L2 cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincaré inequality case and establish a vanishing theorem provided that the weighted function ρ is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighte...  相似文献   

11.
The purpose of this paper is to study a new class of contact manifolds. Such manifolds are called almost f-cosymplectic manifolds. Several tensor conditions are studied for such type of manifolds. We conclude our results with two examples of almost f-cosymplectic manifolds.  相似文献   

12.
Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of non-compact manifolds. Sufficient conditions are established for a class of second order elliptic operators to generate a Feller semigroup on a (generally non-compact) manifold of bounded geometry. A construction of Chernoff approximations is presented for these Feller semigroups in terms of shift operators. This provides approximations of solutions to initial value problems for parabolic equations with variable coefficients on the manifold. It also yields weak convergence of a sequence of random walks on the manifolds to the diffusion processes associated with the elliptic generator. For parallelizable manifolds this result is applied in particular to the representation of Brownian motion on the manifolds as limits of the corresponding random walks.  相似文献   

13.
Almost hypercomplex manifolds with Hermitian and Norden metrics and more specially the corresponding quaternionic Kähler manifolds are considered. Some necessary and sufficient conditions for the investigated manifolds to be isotropic hyper-Kählerian and flat are found. It is proved that the quaternionic Kähler manifolds with the considered metric structure are Einstein for dimension at least 8. The class of the non-hyper-Kähler quaternionic Kähler manifolds of the considered type is determined.  相似文献   

14.
We give a classification of a specific family of seven-dimensional manifolds, the generalized Witten manifolds up to homeomorphism and diffeomorphism. Using an approach suggested by J. Shaneson, we develop a modified surgery theory which fully classifies these manifolds. In contrast to previous approaches, this surgery theory is designed to be more readily applicable to higher dimensions. The family contains examples of manifolds which admit Einstein metrics and are homeomorphic but not diffeomorphic. These particular manifolds occur naturally in differential geometry and are of great interest to both differential geometers and physicists.  相似文献   

15.
Summary The authors try to find necessary and sufficient conditions for the existence of conformal changes of metrics of Riemannian manifolds which implies that the Riemannian manifolds are isometric to spheres. They first obtain a series of integral inequalities in Riemannian manifolds relative to conformal changes of metrics and then find necessary and sufficient conditions under which the Riemannian manifolds are isometric to spheres. Entrata in Redazione il 14 giugno 1976.  相似文献   

16.
In this article we study variable exponent Sobolev spaces on Riemannian manifolds. The spaces are examined in the case of compact manifolds. Continuous and compact embeddings are discussed. The paper contains an example of the application of the theory to elliptic equations on compact manifolds.  相似文献   

17.
In 2006 Masuda and Suh asked if two compact non-singular toric varieties having isomorphic cohomology rings are homeomorphic. In the first part of this paper we discuss this question for topological generalizations of toric varieties, so-called torus manifolds. For example we show that there are homotopy equivalent torus manifolds which are not homeomorphic. Moreover, we characterize those groups which appear as the fundamental groups of locally standard torus manifolds. In the second part we give a classification of quasitoric manifolds and certain six-dimensional torus manifolds up to equivariant diffeomorphism. In the third part we enumerate the number of conjugacy classes of tori in the diffeomorphism group of torus manifolds. For torus manifolds of dimension greater than six there are always infinitely many conjugacy classes. We give examples which show that this does not hold for six-dimensional torus manifolds.  相似文献   

18.
In this paper, we construct a family of three-dimensional asymptotically hyperbolic manifolds with horizons and with scalar curvature equal to −6. The manifolds we construct can be arbitrarily close to anti-de Sitter-Schwarzschild manifolds at infinity. Hence, the mass of our manifolds can be very large or very small. The main arguments we use in this paper are gluing methods which are used by Miao in (Proc Am Math Soc 132(1):217–222, 2004).  相似文献   

19.
Stochastic invariant manifolds are crucial in modelling the dynamical behaviour of dynamical systems under uncertainty. Under the assumption of exponential trichotomy, existence and smoothness of centre manifolds for a class of stochastic evolution equations with linearly multiplicative noise are proved. The exponential attraction and approximation to centre manifolds are also discussed.  相似文献   

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