Can not UndefManifold on complex manifold

[Leo Stein]

Hello,

  This seems like a bug to me. If I create a manifold with Dagger->Complex, UndefManifold will not undefine it since it has visitors:

DefManifold[CM, 8, IndexRange[a, f], Dagger -> Complex]

** DefManifold: Defining manifold CM. 

** DefVBundle: Defining vbundle TangentCM. 

** DefVBundle: Defining conjugated vbundle TangentCM\[Dagger]. Assuming fixed anti-isomorphism between TangentCM and TangentCM\[Dagger]

UndefManifold[CM]

General::noundef: Symbol CM cannot be undefined because it has visitors.

Compare this to the behaviour for a real manifold:

DefManifold[RM, 8, IndexRange[h, m], Dagger -> Real]

** DefManifold: Defining manifold RM. 

** DefVBundle: Defining vbundle TangentRM. 

UndefManifold[RM]

** UndefVBundle: Undefined vbundle TangentRM

** UndefManifold: Undefined manifold RM

Is this an error, or am I misusing DefManifold? That is, can I only declare complex inner VBundles, but not complex tangent VBundles? That would seem too restrictive.

Cheers

Leo

[JMM]

Hi,

There is indeed a restriction. xTensor was originally designed for
real structures, and then generalized to work with inner complex
vector bundles, but has been never been explicitly prepared to handle
complex manifolds, and hence neither complex tangent bundles. That is
why you get an error. DefManifold does not expect (and ignores) the
Dagger option, but passes it to DefVBundle[TangentCM,...] which
defines the complex TangentCM. Then UndefManifold[CM] knows that it
has to undefine TangentCM, but doesn't know that there is a TangentCM\
[Dagger] and hence does not remove it from its list of "visitors". To
solve this, simply do VisitorsOf[CM]^={} before undefining CM. It
would be very simple to fix this, but I'm not sure right now whether
all of xTensor is already compatible with complex manifolds and
tangent bundles, so I will not do it before I decide that.

Cheers,
Jose.

[Leo Stein]

I see! Thanks for your response.

I saw that one can still make complex tensors on the tangent bundle by using DefTensor[..., Dagger->Complex], and this is sufficient for me -- despite not having a complex conjugate VBundle.

Cheers

[Minkyu Park]

Hi all,

Is this problem already solved or still exist?

I guess it is still not fully implemented in current version of xAct 1.1.2, since I got same error message as Leo got.

But Leo, have you ever had some problem with that temporal prescription?

I also have to deal with complex tangent bundle, but it seems there is no way to define complex tangent bundle.

So I just wonder whether you were fine with only complex tensors not complex tangent bundle.

Thanks,

Minkyu

2010년 8월 21일 토요일 오전 2시 4분 43초 UTC+9, Leo C. Stein 님의 말: