bio | website | |
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location | ||
age | 29 | |
visits | member for | 2 years, 10 months |
seen | 1 hour ago | |
stats | profile views | 2,930 |
Hello. I completed my PhD in differential geometry in Edinburgh. I have been reading MathOverflow for a year and a half two and a half years three and a half years.
My primary interests are in $G_2$ and $Spin_7$ geometry.
Nov 17 |
comment |
Isometries of hyper-Kähler manifolds
@BenMcKay, I see the confusion coming from the notation $SO(Im \mathbb{H})$. By this I mean the group of rotations of the $3$-dim real vector space $Im \mathbb{H}$ spanned by the parallel complex structures, not something whose entries lie in $Im \mathbb{H}$. |
Nov 17 |
revised |
Isometries of hyper-Kähler manifolds
Corrected a statement pointed out by a comment, added images and corrected the classification of rotation subgroups. |
Nov 17 |
comment |
Isometries of hyper-Kähler manifolds
@YangMills, I ought to be more careful with my well-known 'facts'. I'll fix it now. |
Nov 9 |
revised |
Isometries of hyper-Kähler manifolds
deleted 58 characters in body |
Nov 9 |
comment |
Isometries of hyper-Kähler manifolds
@RobertBryant, yes of course, I should have noticed that. I have edited the question to clarify. |
Nov 9 |
revised |
Isometries of hyper-Kähler manifolds
added 203 characters in body |
Nov 8 |
awarded | Student |
Nov 8 |
asked | Isometries of hyper-Kähler manifolds |
Oct 29 |
comment |
Dropping the closed requirement from the symplectic manifold definition?
@OldřichSpáčil, I believe it's in Gray and Hervella's The sixteen classes of almost Hermitian manifolds and their linear invariants (1980), but I can't seem to find the paper in my collection (and I don't belong to an institution). You get a finer classification when you have the full almost-Hermitian structure, which is the main part of the paper. The idea is to decompose $\Lambda^3V$ into irreducible reps of the non-compact symplectic group, and apply that to $d\omega$. Similar classifications exist for various other structures, and there are subsequent papers. |
Oct 28 |
comment |
Dropping the closed requirement from the symplectic manifold definition?
While it's true that the condition of admitting such a reduction is topology, once you have one the situation is more geometrical: when $\omega$ is closed there is no local structure but now there is, namely $d\omega$ itself. These geometries can be classified into four types. |
Oct 13 |
comment |
Manifolds admitting flat connections
Related to Q1: mathoverflow.net/questions/91852/… |
Oct 12 |
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Does local reducibility imply global reducibility of universal covering?
You at least need completeness. Otherwise just take any non-rectangular simply connected region in the plane. |
Sep 24 |
awarded | Autobiographer |
May 21 |
comment |
What is an element of an iterated tangent bundle?
@Ryan, e.g. the second order tangent bundle of $\mathcal{M}$ is the vector bundle over $\mathcal{M}$ whose fibre at $p$ consists of $2$-jets at $p$ of curves through $p$. It has rank $n(n+1)/2$ for $n = dim \mathcal{M}$. Just as for the first order tangent bundle, there is also an algebraic definition if you are so minded. |
May 21 |
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What is an element of an iterated tangent bundle?
Whatever name you choose, it shouldn't allow confusion with elements of higher-order tangent bundles (as opposed to iterated ones). |
Apr 26 |
comment |
Relation between kahler potential and Hermitian metric
If $h$ is the Hermitian form, what is the meaning of $\log h$? |
Jan 4 |
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Metalinear frame bundle on sphere or $\mathbb{C}P^n$
What do you want the complex vector bundle $P$ to be for your three spaces? And, given such a $P$, is there not often a choice of such structure? |
Jan 3 |
comment |
Holonomy group of a fiber bundle
I agree with Igor; $M = \{\bullet\}$, $N$ any flat space with non-trivial holonomy and $G$ trivial gives a counterexample. |
Jan 3 |
comment |
Holonomy group of a fiber bundle
Isn't it obvious when using restricted holonomy? |
Jan 3 |
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Holonomy group of a fiber bundle
@Igor, what is the full holonomy group of $[0,1] \times [0,1]$ with opposite sides identified in the usual way? |