Complex contact manifolds and S1 actions

Haydeé Herrera; Rafael Herrera

doi:10.1007/s10711-010-9484-9

Complex contact manifolds and S¹ actions

Haydeé Herrera, Rafael Herrera

Rutgers Camden, Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a curvature condition.

Original language	English (US)
Pages (from-to)	335-345
Number of pages	11
Journal	Geometriae Dedicata
Volume	149
Issue number	1
DOIs	https://doi.org/10.1007/s10711-010-9484-9
State	Published - Dec 2010

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Circle action
Complex contact manifold
Holomorphic Euler characteristic

Access to Document

10.1007/s10711-010-9484-9

Cite this

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title = "Complex contact manifolds and S1 actions",

abstract = "We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a curvature condition.",

keywords = "Circle action, Complex contact manifold, Holomorphic Euler characteristic",

author = "Hayde{\'e} Herrera and Rafael Herrera",

note = "Funding Information: Rafael Herrera, partially supported by a UCMEXUS grant, and CONACYT grants: J48320-F, J110.387/2006.",

year = "2010",

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AU - Herrera, Haydeé

AU - Herrera, Rafael

N1 - Funding Information: Rafael Herrera, partially supported by a UCMEXUS grant, and CONACYT grants: J48320-F, J110.387/2006.

PY - 2010/12

Y1 - 2010/12

N2 - We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a curvature condition.

AB - We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a curvature condition.

KW - Circle action

KW - Complex contact manifold

KW - Holomorphic Euler characteristic

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