Non-orientable three-submanifolds of G2-manifolds
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Leonardo Bagaglini
Abstract
By analogy with associative and co-associative cases, we study a class of three-dimensional non-orientable submanifolds of manifolds with a G2-structure, modelled on planes lying in aspecial G2-orbit. An application of the Cartan–Kähler theory shows that some three-manifolds can be presented in this way. We also classify all the homogeneous ones in ℝℙ7.
Communicated by: T. Leistner
Acknowledgements
The author is grateful to Prof. F. Podestà for all the useful suggestions and conversations he shared with him, to Prof. A. Fino for her constant interest in his work and certainly to “Università degli studi di Firenze” for all the support he received. Finally he wants to thank the anonymous referees for the improvements they suggested.
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- On mixed Lp John ellipsoids
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- A relation between the curvature ellipse and the curvature parabola
- Non-orientable three-submanifolds of G2-manifolds
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Articles in the same Issue
- Frontmatter
- A remark on the mixed scalar curvature of a manifold with two orthogonal totally umbilical distributions
- On mixed Lp John ellipsoids
- Valuations on convex functions and convex sets and Monge–Ampère operators
- Weierstrass points on Kummer extensions
- The Bonnet problem for harmonic maps to the three-sphere
- Maximal arcs in projective planes of order 16 and related designs
- On the decomposition of the small diagonal of a K3 surface
- Doubly transitive dimensional dual hyperovals: universal covers and non-bilinear examples
- Higgs bundles and fundamental group schemes
- A relation between the curvature ellipse and the curvature parabola
- Non-orientable three-submanifolds of G2-manifolds
- The growth of the first non-Euclidean filling volume function of the quaternionic Heisenberg group
- A class of analytic pairs of conjugate functions in dimension three
