共查询到20条相似文献,搜索用时 31 毫秒
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In this paper we give a complete classification of pseudo-Einstein real hypersurfaces in complex two-plane Grassmannians G2(Cm+2). As an application of this result we prove that there do not exist Einstein Hopf or D⊥-invariant Einstein real hypersurfaces in G2(Cm+2). 相似文献
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Let M be a connected complex projective manifold such that c1(T(1,0)M)=0. If M admits a holomorphic Cartan geometry, then we show that M is holomorphically covered by an abelian variety. 相似文献
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Let M be a connected compact quantizable Kähler manifold equipped with a Hamiltonian action of a connected compact Lie group G. Let M//G=?−1(0)/G=M0 be the symplectic quotient at value 0 of the moment map ?. The space M0 may in general not be smooth. It is known that, as vector spaces, there is a natural isomorphism between the quantum Hilbert space over M0 and the G-invariant subspace of the quantum Hilbert space over M. In this paper, without any regularity assumption on the quotient M0, we discuss the relation between the inner products of these two quantum Hilbert spaces under the above natural isomorphism; we establish asymptotic unitarity to leading order in Planck’s constant of a modified map of the above isomorphism under a “metaplectic correction” of the two quantum Hilbert spaces. 相似文献
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In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle Vk to a decreasing family of k foliations Fi on a manifold M. We have shown that there exists a (1,1) tensor J of Vk such that Jk≠0, Jk+1=0 and we defined by LJ(Vk) the Lie Algebra of vector fields X on Vk such that, for each vector field Y on Vk, [X,JY]=J[X,Y]. 相似文献
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Suppose that the sphere Sn has initially a homogeneous distribution of mass and let G be the Lie group of orientation preserving projective diffeomorphisms of Sn. A projective motion of the sphere, that is, a smooth curve in G, is called force free if it is a critical point of the kinetic energy functional. We find explicit examples of force free projective motions of Sn and, more generally, examples of subgroups H of G such that a force free motion initially tangent to H remains in H for all time (in contrast with the previously studied case for conformal motions, this property does not hold for H=SOn+1). The main tool is a Riemannian metric on G, which turns out to be not complete (in particular not invariant, as happens with non-rigid motions), given by the kinetic energy. 相似文献
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We study reduction of generalized complex structures. More precisely, we investigate the following question. Let J be a generalized complex structure on a manifold M, which admits an action of a Lie group G preserving J. Assume that M0 is a G-invariant smooth submanifold and the G-action on M0 is proper and free so that MG?M0/G is a smooth manifold. Under what condition does J descend to a generalized complex structure on MG? We describe a sufficient condition for the reduction to hold, which includes the Marsden–Weinstein reduction of symplectic manifolds and the reduction of the complex structures in Kähler manifolds as special cases. As an application, we study reduction of generalized Kähler manifolds. 相似文献
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Let (M4,g) be a four-dimensional complete noncompact Bach-flat Riemannian manifold with positive Yamabe constant. In this paper, we show that (M4,g) has a constant curvature if it has a nonnegative constant scalar curvature and sufficiently small L2-norm of trace-free Riemannian curvature tensor. Moreover, we get a gap theorem for (M4,g) with positive scalar curvature. 相似文献
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We investigate complete spacelike hypersurfaces in Lorentz–Minkowski space with two distinct principal curvatures and constant mth mean curvature. By using Otsuki’s idea, we obtain the global classification result. As their applications, we obtain some characterizations for hyperbolic cylinders. We prove that the only complete spacelike hypersurfaces in Lorentz–Minkowski (n+1)-spaces (n≥3) of nonzero constant mth mean curvature (m≤n−1) with two distinct principal curvatures λ and μ satisfying inf(λ−μ)2>0 are the hyperbolic cylinders. We also obtain a global characterization for hyperbolic cylinder Hn−1(c)×R in terms of square length of the second fundamental form. 相似文献
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For a simply connected, compact, simple Lie group G, the moduli space of flat G-bundles over a closed surface Σ is known to be pre-quantizable at integer levels. For non-simply connected G, however, integrality of the level is not sufficient for pre-quantization, and this paper determines the obstruction–namely a certain cohomology class in H3(G2;Z)–that places further restrictions on the underlying level. The levels that admit a pre-quantization of the moduli space are determined explicitly for all non-simply connected, compact, simple Lie groups G. 相似文献
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In this paper we show that for a compact minimal hypersurface M of constant scalar curvature in the unit sphere S6 with the shape operator A satisfying ‖A‖2>5, there exists an eigenvalue λ>10 of the Laplace operator of the hypersurface M such that ‖A‖2=λ−5. This gives the next discrete value of ‖A‖2 greater than 0 and 5. 相似文献
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We discuss space-time symmetric Hamiltonian operators of the form H=H0+igH′, where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H′ is invariant under transformation by elements of a subgroup G′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<gc, where gc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g>0. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries. 相似文献
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Let (M,g) be a noncompact complete Bach-flat manifold with positive Yamabe constant. We prove that (M,g) is flat if (M,g) has zero scalar curvature and sufficiently small L2 bound of curvature tensor. When (M,g) has nonconstant scalar curvature, we prove that (M,g) is conformal to the flat space if (M,g) has sufficiently small L2 bound of curvature tensor and L4/3 bound of scalar curvature. 相似文献