共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
We study a class of complex structures on the generalized tangent bundle of a smooth manifold M endowed with a torsion free linear connection, ∇. We introduce the concept of ∇-integrability and we study integrability conditions. In the case of the generalized complex structures introduced by Hitchin (2003) in [2], we compare the two concepts of integrability. Moreover, as an application, we describe almost complex structures on the cotangent bundle of M induced by complex structures on the generalized tangent bundle of M. 相似文献
3.
E. Calviño-Louzao J. Seoane-Bascoy M.E. Vázquez-Abal R. Vázquez-Lorenzo 《Journal of Geometry and Physics》2012
We determine all left-invariant vector fields on three-dimensional Lie groups which define harmonic sections of the corresponding tangent bundles, equipped with the complete lift metric. 相似文献
4.
We generalize the concept of locally symmetric spaces to parabolic contact structures. We show that symmetric normal parabolic contact structures are torsion-free and some types of them have to be locally flat. We prove that each symmetry given at a point with non-zero harmonic curvature is involutive. Finally we give restrictions on the number of different symmetries which can exist at such a point. 相似文献
5.
Here we study geodesics connecting two given points on odd-dimensional spheres respecting the Hopf fibration. This geodesic boundary value problem is completely solved in the case of three-dimensional sphere and some partial results are obtained in the general case. The Carnot–Carathéodory distance is calculated. We also present some motivations related to quantum mechanics. 相似文献
6.
Physical reasons suggested in [J.B. Hartle, S.W. Hawking, Wave function of the universe, Phys. Rev. D41 (1990) 1815–1834] for the Quantum Gravity Problem lead us to study type-changing metrics on a manifold. The most interesting cases are Transverse Riemann–Lorentz Manifolds. Here we study the conformal geometry of such manifolds. 相似文献
7.
Left invariant flat metrics on Lie groups are revisited in terms of left-symmetric algebras which correspond to affine structures. There is a left-symmetric algebraic approach with an explicit formula to the classification theorem given by Milnor. When the positive definiteness of the metric is replaced by nondegeneracy, there are many more examples of left invariant flat pseudo-metrics, which play important roles in several fields in geometry and mathematical physics. We give certain explicit constructions of these structures. Their classification in low dimensions and some interesting examples in higher dimensions are also given. 相似文献
8.
We show that any Weyl curvature model can be geometrically realized by a Weyl manifold. 相似文献
9.
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
10.
11.
12.
13.
We show that R
2n
with its standard symplectic structure is universal in that, subject to a mild topological restriction, essentially all symplectic manifolds can be obtained from it by reduction.Ford Foundation Fellow. Partially supported by NSF grant # DMS-8805699.Supported by the Netherlands Organization for Scientific Research (NWO). 相似文献
14.
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
15.
Let M be a complete surface with parallel mean curvature in a complete simply connected space form F
2+p
(c) of constant curvature c. Denote by H and S the mean curvature and the squared length of the second fundamental form of M respectively. Motivated by L
2-isolation phenomenon in Yang–Mills theory, we prove that if , where c + H
2 > 0, D(H,c) is an explicit positive constant depending on H and c, then , i.e., M is a totally umbilical sphere .
Research supported by the Chinese NSF, Grant No. 10231010; Trans-Century Training Programme Foundation for Talents by the
Ministry of Education of China. 相似文献
16.
The radiation connection induced on an isotropic hypersurface of a Lorentz manifold is described. Consequences for the energy tensor in Einstein field equation are analyzed. A cosmological interpretation is proposed. 相似文献
17.
We prove a lower estimate for the first eigenvalue of the Dirac operator on a compact locally reducible Riemannian spin manifold with positive scalar curvature. We determine also the universal covers of the manifolds on which the smallest possible eigenvalue is attained. 相似文献
18.
19.