Seiberg--Witten-like equations on $5$-dimensional contact metric manifolds | Zendy

Nedim Değirmenci | Zendy; Şenay Bulut | Zendy

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Seiberg--Witten-like equations on $5$-dimensional contact metric manifolds

Author(s) -

Nedim Değirmenci,

Şenay Bulut

Publication year - 2014

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1303-34

Subject(s) - mathematics , spinor , scalar curvature , metric (unit) , manifold (fluid mechanics) , metric connection , spin connection , mathematical analysis , curvature , connection (principal bundle) , spin (aerodynamics) , pure mathematics , dirac equation , mathematical physics , fundamental theorem of riemannian geometry , geometry , physics , gauge theory , mechanical engineering , operations management , engineering , economics , thermodynamics

In this paper, we write Seiberg--Witten-like equations on contact metric manifolds of dimension 5. Since any contact metric manifold has a Spinc-structure, we use the generalized Tanaka--Webster connection on a Spinc spinor bundle of a contact metric manifold to define the Dirac-type operators and write the Dirac equation. The self-duality of 2-forms needed for the curvature equation is defined by using the contact structure. These equations admit a nontrivial solution on 5-dimensional strictly pseudoconvex CR manifolds whose contact distribution has a negative constant scalar curvature.

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