A circle quotient of a $G_2$ cone
| Autor: | Bobby Samir Acharya, Robert L. Bryant, Simon Salamon |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics 53C25 (Primary) 53C28 53C38 81T30 (Secondary) 010102 general mathematics Diagonal Holonomy Fixed point Curvature 01 natural sciences Induced metric Differential Geometry (math.DG) Computational Theory and Mathematics 0103 physical sciences FOS: Mathematics 010307 mathematical physics Geometry and Topology 0101 mathematics Invariant (mathematics) Analysis Quotient Mathematics Symplectic geometry |
| Zdroj: | Acharya, B S, Bryant, R L & Salamon, S 2020, ' A circle quotient of a G2 cone ', DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, vol. 73, 101681 . https://doi.org/10.1016/j.difgeo.2020.101681 |
| DOI: | 10.1016/j.difgeo.2020.101681 |
| Popis: | A study is made of $R^6$ as a singular quotient of the conical space $R^+\times CP^3$ with holonomy $G_2$ with respect to an obvious action by $U(1)$ on $CP^3$ with fixed points. Closed expressions are found for the induced metric, and for both the curvature and symplectic 2-forms characterizing the reduction. All these tensors are invariant by a diagonal action of $SO(3)$ on $R^6$, which can be used effectively to describe the resulting geometrical features. 45 pages, 3 figures. Minor corrections and clarifications, this version accepted for publication in Differential Geometry and its Applications |
| Databáze: | OpenAIRE |
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