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Compact Homogeneous 7-Manifolds Admitting Invariant G2 or ~ G2 -Structures

Thesis Info

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Author

Munir, Muhammadmobeen

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2006

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/779

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725749455

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The main result of this thesis is a classification of all homogeneous spaces G/H admitting a G-invariant G2 -structure, assuming that G is a connected compact Lie group and G acts effectively on G/H. They include a subclass of all homogeneous ̃ spaces G/H with a G-invariant G2 -structure, where G is a compact Lie group. There are many new examples with nontrivial fundamental group. A formula computing the ̃ dimension of the space of G-invariant structures (resp. of G-invariant G2 -structures) on G/H is given. We study a subclass of homogeneous spaces of high rigidity and low rigidity and show that they admit families of invariant co-closed G2 -structures (resp. ̃ ̃ G2 -structures). Some new interesting examples of G2 -structures on these spaces are ̃ found. We also present a scheme of classification of G2 -structures using their intrinsic torsion.
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