Abstract
AbstractWe study the transverse Kähler holonomy groups on Sasaki manifolds (M,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 numberb1(M) and the basic Hodge numberh0,2B(S) vanish, thenSis stable under deformations of the transverse Kähler flow. In addition we show that an irreducible transverse hyperkähler Sasakian structure isS-unstable, whereas, an irreducible transverse Calabi-Yau Sasakian structure isS-stable when dimM≥ 7. Finally, we prove that the standard Sasaki join operation (transverse holonomyU(n1) ×U(n2)) as well as the fiber join operation preserveS-stability.
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