Global Differential Geometry and Global Analysis 1984

Autorentext
Udo Simon: Research Associate, Islamic Studies, University of Heidelberg

Klappentext

A Toponogov splitting theorem for Lorentzian manifolds.- A survey on CR Submanifolds of Kaehlerian manifolds.- Isoperimetric inequalities, heat equation and geometric applications.- Symmetric immersions in pseudo-Riemannian space forms.- Immersions of surfaces into space forms.- Examples of 1-codimensional non totally geodesic isometric immersions of pseudo-riemannian space forms with the same positive constant curvature and the same space-like rank.- Riemannian manifolds with harmonic curvature.- Structure of manifolds of nonpositive curvature.- Equivalence of one dimensional Lagrangian field theories in the plane I.- Applications of the Gauss mapping for hypersurfaces of the sphere.- Submanifolds and the second fundamental tensor.- Embedded minimal surfaces, computer graphics and elliptic functions.- The Bernstein problem for foliations.- Examples concerning the spectrum of a closed Riemannian manifold.- Tight smoothing of some polyhedral surfaces.- On the number of tritangencies of a surface in IR3.- Small eigenvalues of the Laplacian and examples.- Horizontal lifts of isometric immersions into the bundle space of a pseudo-Riemannian submersion.- Positively curved minimal submanifolds.- Affinsph n mit ebenen Schattengrenzen.- Conformal orbits of electromagnetic Riemannian curvature tensors electromagnetic implies gravitational radiation.

Inhalt
A Toponogov splitting theorem for Lorentzian manifolds.- A survey on CR Submanifolds of Kaehlerian manifolds.- Isoperimetric inequalities, heat equation and geometric applications.- Symmetric immersions in pseudo-Riemannian space forms.- Immersions of surfaces into space forms.- Examples of 1-codimensional non totally geodesic isometric immersions of pseudo-riemannian space forms with the same positive constant curvature and the same space-like rank.- Riemannian manifolds with harmonic curvature.- Structure of manifolds of nonpositive curvature.- Equivalence of one dimensional Lagrangian field theories in the plane I.- Applications of the Gauss mapping for hypersurfaces of the sphere.- Submanifolds and the second fundamental tensor.- Embedded minimal surfaces, computer graphics and elliptic functions.- The Bernstein problem for foliations.- Examples concerning the spectrum of a closed Riemannian manifold.- Tight smoothing of some polyhedral surfaces.- On the number of tritangencies of a surface in IR3.- Small eigenvalues of the Laplacian and examples.- Horizontal lifts of isometric immersions into the bundle space of a pseudo-Riemannian submersion.- Positively curved minimal submanifolds.- Affinsphären mit ebenen Schattengrenzen.- Conformal orbits of electromagnetic Riemannian curvature tensors electromagnetic implies gravitational radiation.