On isometric minimal immersion of a singular non-CSC extremal K$\ddot{a}$hler metric into 3-dimensional space forms
Differential Geometry
2022-01-03 v1
Abstract
On any compact Riemann surface there always exists a singular non-CSC (constant scalar curvature) extremal Khler metric which is called a non-CSC HCMU (the Hessian of the Curvature of the Metric is Umbilical) metric. In this paper, by moving frames, we show that any non-CSC HCMU metric can not be isometrically minimal immersed into 3-dimensional real space forms even locally. In general, any non-CSC HCMU metric can not be isometrically immersed into 3-dimensional real space forms with constant mean curvature (CMC).
Keywords
Cite
@article{arxiv.2112.15526,
title = {On isometric minimal immersion of a singular non-CSC extremal K$\ddot{a}$hler metric into 3-dimensional space forms},
author = {Zhiqiang Wei and Yingyi Wu},
journal= {arXiv preprint arXiv:2112.15526},
year = {2022}
}