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- W4287316053 abstract "We study the transverse Kahler holonomy groups on Sasaki manifolds $(M,{oldmathcal S})$ and their stability properties under transverse holomorphic deformations of the characteristic foliation by the Reeb vector field. In particular, we prove that when the first Betti number $b_1(M)$ and the basic Hodge number $h^{0,2}_B({oldmathcal S})$ vanish, then ${oldmathcal S}$ is stable under deformations of the transverse Kahler flow. In addition we show that an irreducible transverse hyperkahler Sasakian structure is ${oldmathcal S}$-unstable, whereas, an irreducible transverse Calabi-Yau Sasakian structure is ${oldmathcal S}$-stable when $dim Mgeq 7$. Finally, we prove that the standard Sasaki join operation (transverse holonomy $U(n_1)times U(n_2)$) as well as the fiber join operation preserve ${oldmathcal S}$-stability." @default.
- W4287316053 created "2022-07-25" @default.
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- W4287316053 date "2021-03-01" @default.
- W4287316053 modified "2023-09-26" @default.
- W4287316053 title "Transverse Kahler holonomy in Sasaki Geometry and ${oldmathcal S}$-Stability" @default.
- W4287316053 doi "https://doi.org/10.48550/arxiv.2103.01112" @default.
- W4287316053 hasPublicationYear "2021" @default.
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