On Ricci flat Supermanifolds | Zendy

Chengang Zhou | Zendy

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On Ricci flat Supermanifolds

Author(s) -

Chengang Zhou

Publication year - 2005

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2005/02/004

Subject(s) - supermanifold , scalar curvature , mathematics , dimension (graph theory) , riemann curvature tensor , pure mathematics , ricci curvature , curvature , flatness (cosmology) , scalar (mathematics) , submanifold , conjecture , ricci flow , mathematical physics , mathematical analysis , geometry , physics , quantum mechanics , cosmology

We study the Ricci flatness condition on generic supermanifolds. It has beenfound recently that when the fermionic complex dimension of the supermanifoldis one the vanishing of the super-Ricci curvature implies the bosonicsubmanifold has vanishing scalar curvature. We prove that this phenomena isonly restricted to fermionic complex dimension one. Further we conjecture thatfor complex fermionic dimension larger than one the Calabi-Yau theorem holdsfor supermanifolds.Comment: 9 pages; typos correcte

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