On Calabi-Yau supermanifolds II
Martin Rocek, Neal Wadhwa
TL;DR
This paper investigates the conditions under which Calabi-Yau supermanifolds with specific dimensions are super Ricci-flat, revealing that compactness implies constant scalar curvature.
Contribution
It provides a classification of Calabi-Yau supermanifolds M(1|2) regarding their super Ricci-flatness and scalar curvature properties.
Findings
Super Ricci-flatness requires the bosonic manifold to have constant scalar curvature.
Compactness of the bosonic manifold constrains its scalar curvature to be constant.
The study advances understanding of geometric conditions for Calabi-Yau supermanifolds.
Abstract
We study when Calabi-Yau supermanifolds M(1|2) with one complex bosonic coordinate and two complex fermionic coordinates are super Ricci-flat, and find that if the bosonic manifold is compact, it must have constant scalar curvature.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory