## Tsukuba Journal of Mathematics

### Helices and isometric immersions

Shigeo Fueki

#### Abstract

Let $f:M\rightarrow\tilde{M}$ be an isometric immersion of a Riemannian manifold $M$ into a Riemannian manifold $\tilde{M}$. We study the geometry of submanifolds under various assumptions with respect to the first curvature $\tilde{\lambda}_{1}$ and the second curvature $\tilde{\lambda}_{2}$ of $\tilde{\sigma}=f\circ\sigma$ in $\tilde{M}$ for a helix $\sigma$ in $M$.

#### Article information

Source
Tsukuba J. Math., Volume 22, Number 2 (1998), 427-445.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496163592

Digital Object Identifier
doi:10.21099/tkbjm/1496163592

Mathematical Reviews number (MathSciNet)
MR1650602

Zentralblatt MATH identifier
0942.53039

#### Citation

Fueki, Shigeo. Helices and isometric immersions. Tsukuba J. Math. 22 (1998), no. 2, 427--445. doi:10.21099/tkbjm/1496163592. https://projecteuclid.org/euclid.tkbjm/1496163592