Spin(7) Metrics of Cohomogeneity One with Aloff–Wallach Spaces as Principal Orbits

Hanci Chi

doi:10.1007/s12220-022-00879-2

Spin(7) Metrics of Cohomogeneity One with Aloff–Wallach Spaces as Principal Orbits

Hanci Chi^*

^*Corresponding author for this work

Department of Foundational Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we construct two continuous 1-parameter family of non-compact Spin (7) metrics with both chiralities, with the principal orbit an Aloff–Wallach space N_k_,_l and the singular orbit CP². For a generic N_k_,_l, metrics constructed are locally asymptotically conical (ALC). For N_{1 , 1}, we construct two continuous 1-parameter families with geometric transition from asymptotically conical (AC) metrics to ALC metrics.

Original language	English
Article number	144
Journal	Journal of Geometric Analysis
Volume	32
Issue number	5
DOIs	https://doi.org/10.1007/s12220-022-00879-2
Publication status	Published - May 2022

Keywords

Aloff–Wallach Space
Cohomogeneity one metrics
Spin(7)Metrics

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10.1007/s12220-022-00879-2

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title = "Spin(7) Metrics of Cohomogeneity One with Aloff–Wallach Spaces as Principal Orbits",

abstract = "In this article, we construct two continuous 1-parameter family of non-compact Spin (7) metrics with both chiralities, with the principal orbit an Aloff–Wallach space Nk,l and the singular orbit CP2. For a generic Nk,l, metrics constructed are locally asymptotically conical (ALC). For N1 , 1, we construct two continuous 1-parameter families with geometric transition from asymptotically conical (AC) metrics to ALC metrics.",

keywords = "Aloff–Wallach Space, Cohomogeneity one metrics, Spin(7)Metrics",

author = "Hanci Chi",

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year = "2022",

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language = "English",

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AU - Chi, Hanci

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N2 - In this article, we construct two continuous 1-parameter family of non-compact Spin (7) metrics with both chiralities, with the principal orbit an Aloff–Wallach space Nk,l and the singular orbit CP2. For a generic Nk,l, metrics constructed are locally asymptotically conical (ALC). For N1 , 1, we construct two continuous 1-parameter families with geometric transition from asymptotically conical (AC) metrics to ALC metrics.

AB - In this article, we construct two continuous 1-parameter family of non-compact Spin (7) metrics with both chiralities, with the principal orbit an Aloff–Wallach space Nk,l and the singular orbit CP2. For a generic Nk,l, metrics constructed are locally asymptotically conical (ALC). For N1 , 1, we construct two continuous 1-parameter families with geometric transition from asymptotically conical (AC) metrics to ALC metrics.

KW - Aloff–Wallach Space

KW - Cohomogeneity one metrics

KW - Spin(7)Metrics

UR - https://www.scopus.com/pages/publications/85125278941

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DO - 10.1007/s12220-022-00879-2

M3 - Article

AN - SCOPUS:85125278941

SN - 1050-6926

VL - 32

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 5

M1 - 144

ER -

Spin(7) Metrics of Cohomogeneity One with Aloff–Wallach Spaces as Principal Orbits

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Keywords

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