On the Kernel of the Equivariant Dirac Operator

Victor Nistor

doi:10.1023/A:1006605923605

On the Kernel of the Equivariant Dirac Operator

Victor Nistor

Mathematics

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7 Scopus citations

Abstract

We prove a vanishing theorem for certain isotypical components of the kernel of the S¹-equivariant Dirac operator with coefficients in an admissible Clifford module. The method is based on changing the metric by a conformal (generally unbounded) factor and studying the effect of this change on the Dirac operator and its kernel. In the cases relevant to S¹-actions we find that the kernel of the new operator is naturally isomorphic to the kernel of the original operator.

Original language	English (US)
Pages (from-to)	595-613
Number of pages	19
Journal	Annals of Global Analysis and Geometry
Volume	17
Issue number	6
DOIs	https://doi.org/10.1023/A:1006605923605
State	Published - 1999

All Science Journal Classification (ASJC) codes

Analysis
Political Science and International Relations
Geometry and Topology

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abstract = "We prove a vanishing theorem for certain isotypical components of the kernel of the S1-equivariant Dirac operator with coefficients in an admissible Clifford module. The method is based on changing the metric by a conformal (generally unbounded) factor and studying the effect of this change on the Dirac operator and its kernel. In the cases relevant to S1-actions we find that the kernel of the new operator is naturally isomorphic to the kernel of the original operator.",

author = "Victor Nistor",

note = "Funding Information: ★ Partially supported an NSF Young Investigator Award DMS-9457859 and a Sloan Research Fellowship. Manuscripts available from http://www.math.psu.edu/nistor/",

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N2 - We prove a vanishing theorem for certain isotypical components of the kernel of the S1-equivariant Dirac operator with coefficients in an admissible Clifford module. The method is based on changing the metric by a conformal (generally unbounded) factor and studying the effect of this change on the Dirac operator and its kernel. In the cases relevant to S1-actions we find that the kernel of the new operator is naturally isomorphic to the kernel of the original operator.

AB - We prove a vanishing theorem for certain isotypical components of the kernel of the S1-equivariant Dirac operator with coefficients in an admissible Clifford module. The method is based on changing the metric by a conformal (generally unbounded) factor and studying the effect of this change on the Dirac operator and its kernel. In the cases relevant to S1-actions we find that the kernel of the new operator is naturally isomorphic to the kernel of the original operator.

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JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

IS - 6

ER -

On the Kernel of the Equivariant Dirac Operator

Abstract

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