On codimension one isometric immersions between indefinite space forms

Minimal Lagrangian isotropic immersions in indefinite complex space forms

Codimension one immersions and the Kervaire invariant one problem

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 ...

Continuous Leafwise Harmonic Functions on Codimension One Transversely Isometric Foliations

Let F be a codimension one foliation on a closed manifold M which admits a transverse dimension one Riemannian foliation. Then any continuous leafwise harmonic functions are shown to be constant on leaves.

Generalized Dpw Method and an Application to Isometric Immersions of Space Forms

Let G be a complex Lie group and ΛG denote the group of maps from the unit circle S into G, of a suitable class. A differentiable map F from a manifold M into ΛG, is said to be of connection order (ba) if the Fourier expansion in the loop parameter λ of the S-family of Maurer-Cartan forms for F , namely F λ dFλ, is of the form P b i=a αiλ . Most integrable systems in geometry are associated to ...