Tsukuba Journal of Mathematics

Minimal immersion of surfaces in quaternionic projective spaces

Abstract

For a minimal immersion of a surface in a quaternionic Kähler manifold a concept of non-degeneracy is defined. Then using a theorem on elliptic differential systems we show a non-degenerate surface is in a sense generic, and around each point with possible exception of an isolated set of degenerate points we can define a smooth Darboux frame. The frame is continuous at a degenerate point. Next, by reducing the structure group we define a symmetric sextic form of type $(6,0)$ and we show in the case that ambient space is $HP^{n}$ this form is a holomorphic (abelian) differential. The last section is a brief note on the relation of our work to Glazebrook's twistor spaces for $HP^{n}$.

Article information

Source
Tsukuba J. Math., Volume 12, Number 2 (1988), 423-440.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496160839

Digital Object Identifier
doi:10.21099/tkbjm/1496160839

Mathematical Reviews number (MathSciNet)
MR968201

Zentralblatt MATH identifier
0663.53043

Citation

Zandi, Ahmad. Minimal immersion of surfaces in quaternionic projective spaces. Tsukuba J. Math. 12 (1988), no. 2, 423--440. doi:10.21099/tkbjm/1496160839. https://projecteuclid.org/euclid.tkbjm/1496160839