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51.
Erwann Delay 《Advances in Mathematics》2002,168(2):213-224
On an asymptotically hyperbolic Einstein manifold (M,g0) for which the Yamabe invariant of the conformal structure on the boundary at infinity is nonnegative, we show that the operators of Ricci curvature, and of Einstein curvature, are locally invertible in a neighborhood of the metric g0. We deduce in the C∞ case that the image of the Riemann-Christoffel curvature operator is a submanifold in a neighborhood of g0. 相似文献
52.
Hui Li 《Proceedings of the American Mathematical Society》2003,131(11):3579-3582
Let be a connected, compact symplectic manifold equipped with a Hamiltonian action. We prove that, as fundamental groups of topological spaces, , where is the symplectic quotient at any value in the image of the moment map .
53.
Harald Biller 《Transactions of the American Mathematical Society》2003,355(1):407-432
Essential results about actions of compact Lie groups on connected manifolds are generalized to proper actions of arbitrary groups on connected cohomology manifolds. Slices are replaced by certain fiber bundle structures on orbit neighborhoods. The group dimension is shown to be effectively finite. The orbits of maximal dimension form a dense open connected subset. If some orbit has codimension at most , then the group is effectively a Lie group.
54.
Thetheoryofharmonicmapsintoacompactnonpositivelycurvedtargetiswell-developed.TheexistenceofsuchaharmonicmappinginanygivenhomotopyclassisestablishedbyEellsandSampson[1]in1964,andlater,in1967,Hartman[2]gaveaproofoftheuniqueness.Thispaperisdevotedtoanapplicationo… 相似文献
55.
56.
本文给出了强K(a)hler-Finsler流形上中值Laplace算子的一些性质,如自伴性质,散度形式等.与K(a)hler流形上利用逆变基本张量[11]及其在Finsler流形上的变形[5,10]作为密度函数定义流形上的逐点内积及整体内积不同,作者利用强K(a)hler-Finsler流形上的逆变密切Kahler度量作为密度函数定义了流形上的逐点内积和整体内积,并定义了强K(a)hler-Finsler流形上的Hodge-Laplace算子,它可看作函数情形中值Laplace算子的推广. 相似文献
57.
This paper considers the exponential decay of the solution to a damped semilinear wave equation with variable coefficients in the principal part by Riemannian multiplier method. A differential geometric condition that ensures the exponential decay is obtained. 相似文献
58.
Jonathan Spreer 《Discrete Mathematics》2011,(14):1295
We investigate slicings of combinatorial manifolds as properly embedded co-dimension 1 submanifolds. Focus is given to the case of dimension 3, where slicings are (discrete) normal surfaces. For the cases of 2-neighborly 3-manifolds as well as quadrangulated slicings, lower bounds on the number of quadrilaterals of slicings depending on its genus g are presented. These are shown to be sharp for infinitely many values of g. Furthermore, we classify slicings of combinatorial 3-manifolds which are weakly neighborly polyhedral maps. 相似文献
59.
We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite nearly K ¨ahler manifold and obtain characterization theorems for holo-morphic sectional and holomorphic bisectional curvature. We also establish a condi-tion for a GCR-lightlike submanifold of an indefinite complex space form to be a null holomorphically flat. 相似文献
60.
We deal with complete hypersurfaces immersed in a semi-Riemannian warped product of the type eI×f M~n,where M~n is a connected n-dimensional oriented Riemannian manifold.When the fiber M~n is complete with sectional curvature-k≤K_M for some positive constant k,under appropriate restrictions on the norm of the gradient of the height function h,we proceed with our technique in order to guarantee that complete hypersurface immersed in a semi-Riemannian warped product is a slice.Our approach is based on the well known generalized maximum principle and another suitable maximum principle at the infinity due to Yau. 相似文献