Transverse Kähler holonomy in Sasaki Geometry and S-Stability

We 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 number b1(M) and the basic Hodge number h0,2B...

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Autores principales:	Boyer Charles P., Huang Hongnian, Tønnesen-Friedman Christina W.
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	algebraic deformations transverse kähler sasakian transverse holonomy 53c25 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/6ea17538c719424b9149507b1b3dce17
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spelling	oai:doaj.org-article:6ea17538c719424b9149507b1b3dce172021-12-05T14:10:45ZTransverse Kähler holonomy in Sasaki Geometry and S-Stability2300-744310.1515/coma-2020-0123https://doaj.org/article/6ea17538c719424b9149507b1b3dce172021-11-01T00:00:00Zhttps://doi.org/10.1515/coma-2020-0123https://doaj.org/toc/2300-7443We 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 number b1(M) and the basic Hodge number h0,2B(S) vanish, then S is stable under deformations of the transverse Kähler flow. In addition we show that an irreducible transverse hyperkähler Sasakian structure is S-unstable, whereas, an irreducible transverse Calabi-Yau Sasakian structure is S-stable when dim M ≥ 7. Finally, we prove that the standard Sasaki join operation (transverse holonomy U(n1) × U(n2)) as well as the fiber join operation preserve S-stability.Boyer Charles P.Huang HongnianTønnesen-Friedman Christina W.De Gruyterarticlealgebraicdeformationstransverse kählersasakiantransverse holonomy53c25MathematicsQA1-939ENComplex Manifolds, Vol 8, Iss 1, Pp 336-353 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	algebraic deformations transverse kähler sasakian transverse holonomy 53c25 Mathematics QA1-939
spellingShingle	algebraic deformations transverse kähler sasakian transverse holonomy 53c25 Mathematics QA1-939 Boyer Charles P. Huang Hongnian Tønnesen-Friedman Christina W. Transverse Kähler holonomy in Sasaki Geometry and S-Stability
description	We 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 number b1(M) and the basic Hodge number h0,2B(S) vanish, then S is stable under deformations of the transverse Kähler flow. In addition we show that an irreducible transverse hyperkähler Sasakian structure is S-unstable, whereas, an irreducible transverse Calabi-Yau Sasakian structure is S-stable when dim M ≥ 7. Finally, we prove that the standard Sasaki join operation (transverse holonomy U(n1) × U(n2)) as well as the fiber join operation preserve S-stability.
format	article
author	Boyer Charles P. Huang Hongnian Tønnesen-Friedman Christina W.
author_facet	Boyer Charles P. Huang Hongnian Tønnesen-Friedman Christina W.
author_sort	Boyer Charles P.
title	Transverse Kähler holonomy in Sasaki Geometry and S-Stability
title_short	Transverse Kähler holonomy in Sasaki Geometry and S-Stability
title_full	Transverse Kähler holonomy in Sasaki Geometry and S-Stability
title_fullStr	Transverse Kähler holonomy in Sasaki Geometry and S-Stability
title_full_unstemmed	Transverse Kähler holonomy in Sasaki Geometry and S-Stability
title_sort	transverse kähler holonomy in sasaki geometry and s-stability
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/6ea17538c719424b9149507b1b3dce17
work_keys_str_mv	AT boyercharlesp transversekahlerholonomyinsasakigeometryandsstability AT huanghongnian transversekahlerholonomyinsasakigeometryandsstability AT tønnesenfriedmanchristinaw transversekahlerholonomyinsasakigeometryandsstability
_version_	1718371763906150400

Transverse Kähler holonomy in Sasaki Geometry and S-Stability

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