Results 1 - 10 of 5848
Results 1 - 10 of 5848. Search took: 0.033 seconds
|Sort by: date | relevance|
[en] The question considered is whether or not a Riemannian metric can be found to make a given curve field on a closed surface into geodesics. Allowing singularities removes the restriction to Euler characteristic zero. The main results are the following: only two types of isolated singularities can occur in a geodesic field on a surface. No geodsic fields exist on a surface with Euler characteristic less than zero. If the Euler characteristic is zero, such a geodesic field can have only removable singularities. Only a limited number of geodesic fields exist on S2 and RP2. A closed geodesic (perhaps made from several curves and singularities) always appears in such a field
[en] This note follows a previous note on the existence of space-like maximal submanifolds in a hyperbolic riemannian differentiable manifold. It contains some uniqueness and non-existence theorems, and a study of the maximisation of area by such a submanifold
[fr]On demontre quelques proprietes (theoremes d'unicite, de non-existence, de maximisation de l'aire) des sous-varietes maximales, ou a courbure moyenne extrinseque constante d'une variete differentiable munie d'une metrique riemannienne hyperbolique
[en] The hypersurfaces of En+1 have been studied for the particular case when they satisfy the R.C-condition or the C.R-condition. One objective is to generalize this situation to a higher codimension. More precisely, we consider the case of dimension 4, and replace the condition of quasiumbilicity by the conformal flatness. In this way, we construct an example of 4-submanifold of IE6 which is conformally flat at a particular point without being quasiumbilical. That such submanifolds exist, was asserted without proof. Thus, we present another counter-example. (author). 4 refs
[en] Cauchy and exponential transforms are characterized, and constructed, as canonical holomorphic sections of certain line bundles on the Riemann sphere defined in terms of the Schwarz function. A well known natural connection between Schwarz reflection and line bundles defined on the Schottky double of a planar domain is briefly discussed in the same context.
[en] 1. Cohomology of vector bundles and the duality theorem. 2. Divisors, line bundles and the Riemann-Roch theorem. 3. Projective embedding of a compact Riemann surface. 4. Genus and first Betti number. 5. Chern class and degree. 6. The Jacobian. 7. Line bundles and characters. 8. Poincare bundle. 9. The Picard manifold of a compact Kaehler manifold. 10. Vector bundles on a compact Riemann surface. 11. The Riemann-Roch theorem for vector bundles. 12. Indecomposable bundles and the Krull-Remak-Schmidt theorem. 13. Weil's theorem; unitary bundles. Appendix: Factors of automorphy. (author)
[en] Every branched superminimal surface of area 4πd in S4 is shown to arise from a pair of meromorphic functions (f1,f2) of bidegree (d,d) such that f1 and f2 have the same ramification divisor. Conditions under which branched superminimal surfaces can be generated from such pairs of functions are derived. For each d ≥ 1 the space of harmonic maps (i.e branched superminimal immersions) of S2 into S4 of harmonic degree d is shown to be a connected space of complex dimension 2d+4. (author). 18 refs
[en] In this paper, we will prove vanishing and finiteness theorems for -harmonic 1-forms on a locally conformally flat Riemannian manifold under the assumptions on the Schrödinger operators involving the squared norm of the traceless Ricci form. From these theorems and the work of Li–Tam, we can obtain some one-end and finite ends results for the locally conformally flat Riemannian manifold.
[en] It is proved that for n≥3 there exists a constant δ(n) with 1/4≤δ(n)<1 such that if M is a simply connected Riemannian manifold of dimension n with δ(n)-pinched curvatures then for every Riemannian manifold N every stable harmonic map Φ:M→N is constant. Together with Howard's result, it shows that a simply connected sufficiently pinched Riemannian manifold is weakly E-unstable. (author). 8 refs
[en] Riemann matrices occur naturally as period matrices of closed Riemann surfaces and of multiply periodic meromorphic functions. In this expository paper some of the basic properties of such matrices are reviewed in order to point out an area of open problems and draw attention to the beautiful and profound work of Hayashida and Nishi. (author)
[en] The results of this work are referred to the well-known trend of the geometric theory of functions of complex variable, namely, to the extreme problems on the classes of nonoverlapping domains. It was started by Lavrent’ev’s classical work , where, in particular, the problem of the product of conformal radii of two nonoverlapping domains was first solved. Now, this trend is intensively developed. The main results can be found in [2–8] and [9–13]. Our results present a generalization of some results in .