By D. Ferus, U. Simon, U. Pinkall, B. Wegner
All papers showing during this quantity are unique study articles and feature now not been released somewhere else. They meet the necessities which are valuable for e-book in a quality basic magazine. E.Belchev, S.Hineva: at the minimum hypersurfaces of a in the community symmetric manifold. -N.Blasic, N.Bokan, P.Gilkey: The spectral geometry of the Laplacian and the conformal Laplacian for manifolds with boundary. -J.Bolton, W.M.Oxbury, L.Vrancken, L.M. Woodward: minimum immersions of RP2 into CPn. -W.Cieslak, A. Miernowski, W.Mozgawa: Isoptics of a strictly convex curve. -F.Dillen, L.Vrancken: Generalized Cayley surfaces. -A.Ferrandez, O.J.Garay, P.Lucas: On a definite category of conformally flat Euclidean hypersurfaces. -P.Gauduchon: Self-dual manifolds with non-negative Ricci operator. -B.Hajduk: at the obstruction team toexistence of Riemannian metrics of optimistic scalar curvature. -U.Hammenstaedt: Compact manifolds with 1/4-pinched adverse curvature. -J.Jost, Xiaowei Peng: The geometry of moduli areas of reliable vector bundles over Riemannian surfaces. - O.Kowalski, F.Tricerri: A canonical connection for in the neighborhood homogeneous Riemannian manifolds. -M.Kozlowski: a few fallacious affine spheres in A3. -R.Kusner: A greatest precept at infinity and the topology of whole embedded surfaces with consistent suggest curvature. -Anmin Li: Affine completeness and Euclidean completeness. -U.Lumiste: On submanifolds with parallel larger order basic shape in Euclidean areas. -A.Martinez, F.Milan: Convex affine surfaces with consistent affine suggest curvature. -M.Min-Oo, E.A.Ruh, P.Tondeur: Transversal curvature and tautness for Riemannian foliations. -S.Montiel, A.Ros: Schroedinger operators linked to a holomorphic map. -D.Motreanu: commonplace lifestyles of Morse capabilities on countless dimensional Riemannian manifolds and purposes. -B.Opozda: a few extensions of Radon's theorem.
Read or Download Global Differential Geometry and Global Analysis: Proceedings, Berlin 1991 PDF
Similar geometry and topology books
This guide bargains with the principles of prevalence geometry, in courting with department earrings, jewelry, algebras, lattices, teams, topology, graphs, good judgment and its self reliant improvement from quite a few viewpoints. Projective and affine geometry are coated in quite a few methods. significant periods of rank 2 geometries corresponding to generalized polygons and partial geometries are surveyed generally.
Convex research is the calculus of inequalities whereas Convex Optimization is its program. research is inherently the area of the mathematician whereas Optimization belongs to the engineer. In layman's phrases, the mathematical technology of Optimization is the learn of the way to make a sensible choice while faced with conflicting requisites.
Extra resources for Global Differential Geometry and Global Analysis: Proceedings, Berlin 1991
First, we assume that 111 is not empty. Then 111 is a non empty open part of M and in each point p of Ill, we know that (Vh)p = 0. The classical Pick-Berwald theorem then implies that 111 is an open part of a nondegenerate ellipsoid or hyperboloid. Thus detS is a constant different from zero on 111" The continuity of detS then implies that fit = M. Finally, we may assume that S = 0 on the whole of M. Thus by Proposition 2, we can suppose that M is given by the equation z -- P(x,y), where P is a polynomial of degree at most k + 1, and that the canonical affine normal vector field is given by (0,0,1).
N be the Frenet frame of its directrix curve ~o" through ~p2 if and only if (i) n = 2m, (ii) ~ = ~m, (iii) ~o(z) Theorem 5 where z is a stereographic complex coordinate. - ~n(-I/~) be a linearly full minimal L e t %b : S 2 --+ CP n, n - 2m, immersion which factors through ~P~, ~o is k-point ramified for k < 2. and suppose that the directrix curve Let z be a stereographic complex coordinate such that if k ~ 0 then 4o has a higher order singularity at z - O. Then ~o is given by g/o(Z) = /kp zk' + ' " "+ kp ep (t) p-O where e_o .
Remark The condition of factoring through RP 2 is crucial here. result is not true in general. [l]). This, together with Theorem 2, is a first step in dealing with the space of minimal immersions of S ~ into Sn. Finally, combining Theorems 2 and 6, we have the following partial generalisation of Theorem 5. Theorem 7 Let # : S ~ --+ CP n be a linearly full minimal immersion which factors through Rp2. Then up to holomorphic isometries of CP n there are only finitely many minimal immersions of S 2 into CP n which factor through ~p2 and have the same singularity type as ~.
Global Differential Geometry and Global Analysis: Proceedings, Berlin 1991 by D. Ferus, U. Simon, U. Pinkall, B. Wegner