Isometric immersions in symmetric spaces

Tight Equivariant Immersions of Symmetric Spaces

Introduction. Let G/K be a compact, irreducible symmetric space and Q = f+p the Lie algebra of G. If ir is a non trivial real class-one representation of G on E with O^e, infixed, then the map TlG/K —*E given by gK—*ir{g)e gives an immersion of G/K into E. The purpose of this note is to announce the classification of such immersions with minimal absolute curvature (i.e., are tight) [ l ] , [4]....

Minimal Immersions of Symmetric Spaces into Spheres

On Local Isometric Immersions into Complex and Quaternionic Projective Spaces

We will prove that if an open subset of CPn is isometrically immersed into CPm, withm < (4/3)n−2/3, then the image is totally geodesic. We will also prove that if an open subset of HPn isometrically immersed into HPm, with m < (4/3)n− 5/6, then the image is totally geodesic.

On isometric Lagrangian immersions

This article uses Cartan-Kähler theory to show that a small neighborhood of a point in any surface with a Riemannian metric possesses an isometric Lagrangian immersion into the complex plane (or by the same argument, into any Kähler surface). In fact, such immersions depend on two functions of a single variable. On the other hand, explicit examples are given of Riemannian three-manifolds which ...

Isometric Immersions and Compensated Compactness

A fundamental problem in differential geometry is to characterize intrinsic metrics on a two-dimensional Riemannian manifold M2 which can be realized as isometric immersions into R3. This problem can be formulated as initial and/or boundary value problems for a system of nonlinear partial differential equations of mixed elliptic-hyperbolic type whose mathematical theory is largely incomplete. I...