## Tsukuba Journal of Mathematics

### Lagrangian $H$-umbilical submanifolds in quaternion Euclidean spaces

#### Abstract

In [2], B. Y. Chen proved that the Lagrangian $H$-umbilical submanifolds in complex Euclidean space C$^{n}$ are Lagrangian pseudospheres and complex extensors of the unit hypersphere of E$^{n}$, except the flat ones. Similar to this, we can define the Lagrangian $H$-umbilical submanifold in quatemion space forms. The main purpose of this paper is to classify the Lagrangian $H$-umbilical submanifolds in quatemion Euclidean space H$^{n}$.

#### Article information

Source
Tsukuba J. Math., Volume 29, Number 1 (2005), 233-245.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496164901

Digital Object Identifier
doi:10.21099/tkbjm/1496164901

Mathematical Reviews number (MathSciNet)
MR2162838

Zentralblatt MATH identifier
1098.53050

#### Citation

Oh, Yun Myung; Kang, Joon Hyuk. Lagrangian $H$-umbilical submanifolds in quaternion Euclidean spaces. Tsukuba J. Math. 29 (2005), no. 1, 233--245. doi:10.21099/tkbjm/1496164901. https://projecteuclid.org/euclid.tkbjm/1496164901