Existence of Horizontal Immersions in Fat Distributions

evaluation of fat atrophy in patients with dermis fat graft of orbit by ct-scan

چکیده ندارد.

The Existence of Minimal Immersions of 2-Spheres

Existence of isometric immersions into nilpotent Lie groups

We establish necessary and sufficient conditions for existence of isometric immersions of a simply connected Riemannian manifold into a two-step nilpotent Lie group. This comprises the case of immersions into H-type groups. MSC 2000: 53C42, 53C30

An Existence Theorem for G-structure Preserving Affine Immersions

We prove an existence result for local and global G-structure preserving affine immersions between affine manifolds. Several examples are discussed in the context of Riemannian and semi-Riemannian geometry, including the case of isometric immersions into Lie groups endowed with a left-invariant metric, and the case of isometric immersions into products of space forms.

Intrinsic Obstructions to the Existence of Isometric Minimal Immersions

S.S. Chern raised the problem to find necessary and sufficient conditions for a given Riemannian manifold to be realizable on a minimal submanifold of a Euclidean space. The aim of this paper is to provide new necessary conditions. For minimal submanifolds in a Euclidean space we consider the negative of the Ricci tensor as defining a new metric, which is nothing but the third fundamental form,...