On cohomogeneity one Hermitian non-Kähler metrics
نویسندگان
چکیده
We investigate the geometry of Hermitian manifolds endowed with a compact Lie group action by holomorphic isometries principal orbits codimension one. In particular, we focus on special class these constructed following B\'erard-Bergery which includes, among others, line bundles $\mathbb C\mathbb P^{m-1}$, linear Hopf and Hirzebruch surfaces. characterize their invariant metrics, such as balanced, K\"ahler-like, pluriclosed, locally conformally K\"ahler, Vaisman, Gauduchon. Furthermore, construct new examples cohomogeneity one metrics solving second-Chern-Einstein equation constant Chern-scalar curvature equation.
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ژورنال
عنوان ژورنال: Proceedings
سال: 2022
ISSN: ['0890-1740']
DOI: https://doi.org/10.1017/prm.2022.5