𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Deformation of a submanifold in an Euclidean space with fixed Gauss image

✍ Scribed by Yosio Mutō

Publisher
Springer
Year
1981
Tongue
English
Weight
689 KB
Volume
11
Category
Article
ISSN
0046-5755

No coin nor oath required. For personal study only.

✦ Synopsis

In a previous paper [4] the present author studied a C °~ mapping ~: M x I ~ R" where M is an m-dimensional C ® manifold, I is some interval and for each t E I the mapping ],: M x t-o Rn is an immersion satisfying the following conditions, (i) The Gauss map associated with the immersion is regular. (ii) The Gauss image of the immersed submanifold is fixed against t for each point p of M. Such a mapping £ was called an admissible deformation. The purpose of the present paper is to give results obtained since then.

📜 SIMILAR VOLUMES

An estimate on the total curvature of a
An estimate on the total curvature of a geodesic in Euclidean 3-space-with-boundary
✍ I. D. Berg 📂 Article 📅 1982 🏛 Springer 🌐 English ⚖ 321 KB

In this note we show that the total curvature of a geodesic in the manifoldwith-boundary consisting of Euclidean 3-space with a boundary of the form z = f(x, y) has a bound of at most 2p iff satisfies a Lipschitz condition with the Lipschitz constant at most p. This global result immediately yields