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71.
We give a reduction procedure to determine (locally) the surfaces with constant Gauss curvature in a three-dimensional manifold which are invariant under the action of a one-parameter subgroup of the isometry group of the ambient space. We apply this procedure to describe the invariant surfaces with constant Gauss curvature in and in . 相似文献
72.
P. Delorme 《Journal of Functional Analysis》2004,217(2):314-346
We introduce a filtration of a -module of some space of functions on a reductive symmetric space G/H, and compute the associated grading as a direct sum of induced representations. As an application of this result to the reductive groups viewed as symmetric spaces, we are able to realize any Harish-Chandra module as a subquotient of a direct sum of induced representations from parabolic subgroups, the inducing representations being trivial on the unipotent radical. 相似文献
73.
Existence and asymptotic stability for evolution problems on manifolds with damping and source terms
Marcelo M. Cavalcanti Valéria N. Domingos Cavalcanti 《Journal of Mathematical Analysis and Applications》2004,291(1):109-127
One considers the nonlinear evolution equation with source and damping terms
74.
Let X be a Polish space and P a Markov operator acting on the space of Borel measures on X. We will prove the existence of an invariant measure with respect to P, provided that P satisfies some condition of a Prokhorov type and that the family of functions is equi-continuous with respect to the Prokhorov distance at some point of the space X. Moreover, we will construct a counterexample which show that the above equi-continuity condition cannot be dropped. 相似文献
75.
Integrated Density of States For Random Metrics on Manifolds 总被引:3,自引:0,他引:3
Lenz Daniel; Peyerimhoff Norbert; Veselic Ivan 《Proceedings London Mathematical Society》2004,88(3):733-752
We study ergodic random Schrödinger operators on a coveringmanifold, where the randomness enters both via the potentialand the metric. We prove measurability of the random operators,almost sure constancy of their spectral properties, the existenceof a self-averaging integrated density of states and a Pasturubintype trace formula. 2000 Mathematics Subjects Classification35J10, 58J35, 82B44. 相似文献
76.
Boris Rubin 《Transactions of the American Mathematical Society》2004,356(12):5045-5070
We develop an analytic approach to the Radon transform , where is a function on the affine Grassmann manifold of -dimensional planes in , and is a -dimensional plane in the similar manifold k$">. For , we prove that this transform is finite almost everywhere on if and only if , and obtain explicit inversion formulas. We establish correspondence between Radon transforms on affine Grassmann manifolds and similar transforms on standard Grassmann manifolds of linear subspaces of . It is proved that the dual Radon transform can be explicitly inverted for , and interpreted as a direct, ``quasi-orthogonal" Radon transform for another pair of affine Grassmannians. As a consequence we obtain that the Radon transform and the dual Radon transform are injective simultaneously if and only if . The investigation is carried out for locally integrable and continuous functions satisfying natural weak conditions at infinity.
77.
Let X be a Hopf manifolds with an Abelian fundamental group. E is a holomorphic vector bundle of rank r with trivial pull-back to W = ℂ
n
–{0}. We prove the existence of a non-vanishing section of L⊗E for some line bundle on X and study the vector bundles filtration structure of E. These generalize the results of D. Mall about structure theorem of such a vector bundle E.
The research was supported by 973 Project Foundation of China and the Outstanding Youth Science Grant of NSFC (grant no. 19825105) 相似文献
78.
We address the problem of the separation of variables for the Hamilton–Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called N manifolds, to give intrisic tests of separability (and Stäckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel'fand–Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations. 相似文献
79.
Andrea Iannuzzi 《Proceedings of the American Mathematical Society》2003,131(12):3839-3843
Let act by biholomorphisms on a taut manifold . We show that can be regarded as a -invariant domain in a complex manifold on which the universal complexification of acts. If is also Stein, an analogous result holds for actions of a larger class of real Lie groups containing, e.g., abelian and certain nilpotent ones. In this case the question of Steinness of is discussed.
80.
A family of subspaces of a complex separable Hilbert space is transitive if every bounded operator which leaves each of its
members invariant is scalar. This article surveys some results concerning transitive families of small cardinality, and adds
some new ones. The minimum cardinality of a transitive family in finite dimensions (greater than 2) is 4. In infinite dimensions
a transitive pair of linear manifolds exists but the minimum cardinality of a transitive family of dense operator ranges or
norm-closed subspaces is not known. However, a transitive family of dense operator ranges with 5 elements can be found, and
so can a transitive family of norm-closed subspaces with 4 elements. In finite dimensions (> 1) three nest algebras (corresponding
to maximal nests) can intersect in the scalar operators, but two cannot. It is not known if this is the case in infinite dimensions
for maximal nests of type ω + 1. Four such nest algebras can intersect in the scalar operators.
Received June 15, 2002, Accepted November 27, 2002 相似文献