Any smooth connected non-orientable manifold is equipped with a real line bundle of order two. Various structures which are defined only on oriented manifolds extend to non-orientable manifolds once they are twisted by this line bundle of order two. Our aim is to develop this theme....
Let M be a manifold of dimension n which is immersible in Rn+1 . Then T c M is trivial if M is orientable, or M is non-orientable with H 2 (M , Z) = 0. In fact, Gromov proved a stronger result that M admits an exact Lagrangian immersion in Euclidean space when M is ...
We study complex hyperbolic disc bundles over closed orientable surfaces that arise from discrete and faithful representations H_n->PU(2,1), where H_n is t... S Anan'In,CH Grossi,N Gusevskii - 《International Mathematics Research Notices》 被引量: 50发表: 2005年 On the volumes of comple...
摘要: We study the complex symplectic geometry of the space Q(S) of the quasifuchsian structures of a closed Riemannian surface S of genus g>1. We prove that this space is a flat complex symplectic manifold and we describe the hamiltonian nature of the quasifuchsian bending vector fields....
$U(n+1)\times U(p+1)$ -Hermitian Metrics on the Manifold $S^{2n+1}\times S^{2p+1}$ A two-parameter family of invariant almost-complex structures is given on the homogeneous space ; all these structures are integrable. We consider all inva... NA Daurtseva - 《Mathematical Notes》...
The latter is a class of flat orientable n-dimensional manifolds with holonomy group Z2n−1, a generalisation of the original Hantzsche-Wendt manifold which is the unique 3-dimensional manifold with holonomy group Z22. Any Hantzsche-Wendt manifold is odd-dimensional, thus it cannot be a ...
Every manifold admits a nowhere vanishing complex vector field. If, however, the manifold is compact and orientable and the complex bilinear form associated to a Riemannian metric is never zero when evaluated on the vector field, then the manifold must have zero Euler characteristic....
When the submanifold is orientable, these estimates were proved by A. Raich in =-=[33]-=- using microlocal methods. Our proof deduces the estimates from (a slight extension, when q > 1, of) those known on hypersurfaces via the fact that locally, CR-submanifolds of hypersurface type are...
3-manifoldComplex-valued characteristic invariantCharacteristic holomorphic functionA complete invariant defined for (closed, connected, orientable) 3-manifolds is an invariant defined for the 3-manifolds such that any two 3-manifolds with the same invariant are homeomorphic. Further, if the 3-manifold...
Moreover, if ~,~ is a real-analytic orientable codimension-one foliation of a three-dimensional real manifold S then the following argument shows that (S, ~) does indeed arise as a Levi-foliation. First we choose a real-analytic metric on S [G]; the induced conformal structure on the ...