Associative Submanifolds of the Berger Space
We study associative submanifolds of the Berger space SO(5)/SO(3) endowed with its homogeneous nearly-parallel G2-structure. We focus on two geometrically interesting classes: the ruled associatives, and the associatives with special Gauss map. We show that the associative submanifolds ruled by a ce...
Saved in:
Main Authors | , |
---|---|
Format | Journal Article |
Language | English |
Published |
29.03.2020
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | We study associative submanifolds of the Berger space SO(5)/SO(3) endowed
with its homogeneous nearly-parallel G2-structure. We focus on two
geometrically interesting classes: the ruled associatives, and the associatives
with special Gauss map.
We show that the associative submanifolds ruled by a certain special type of
geodesic are in correspondence with pseudo-holomorphic curves in
$Gr_2^+(TS^4).$ Using this correspondence, together with a theorem of Bryant on
superminimal surfaces in $S^4,$ we prove the existence of infinitely many
topological types of compact immersed associative 3-folds in SO(5)/SO(3).
An associative submanifold of the Berger space is said to have special Gauss
map if its tangent spaces have non-trivial SO(3)-stabiliser. We classify the
associative submanifolds with special Gauss map in the cases where the
stabiliser contains an element of order greater than 2. In particular, we find
several homogeneous examples of this type. |
---|---|
DOI: | 10.48550/arxiv.2003.13169 |