## Tsukuba Journal of Mathematics

### Unstable harmonic maps into real hypersurfaces of a complex Hopf manifold

#### Abstract

Let $\phi: M\rightarrow N$ be a pseudohermitian immersion ([6]) of a compact strictly pseudoconvex $CR$ manifold $M$ into a totally umbilical real hypersurface $N$, of nonzero mean curvature of $(\Vert H\Vert\neq 0)$, of a complex Hopf manifold $\bm{C}H^{n}$, tangent to the Lee field $B_{0}$ of $\bm{C}H^{n}$. If $B_{0}$ is orthogonal to the $CR$ structure of $N$ and $E(\phi) \gt \mathop{V\!ol}(M)/[(1+\Vert H\Vert^{2})\Vert H\Vert^{2}]$ then $\phi$ is an unstable harmonic map.

#### Article information

Source
Tsukuba J. Math., Volume 25, Number 1 (2001), 203-213.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496164221

Digital Object Identifier
doi:10.21099/tkbjm/1496164221

Mathematical Reviews number (MathSciNet)
MR1846877

Zentralblatt MATH identifier
1011.53047

#### Citation

Dragomir, Sorin; Enea, Maria Rosaria. Unstable harmonic maps into real hypersurfaces of a complex Hopf manifold. Tsukuba J. Math. 25 (2001), no. 1, 203--213. doi:10.21099/tkbjm/1496164221. https://projecteuclid.org/euclid.tkbjm/1496164221