Okay, so the second speaker is Dr. Hans from the African Institute of Mathematical Sciences

and the University of Douala, who is actually visiting us now in FRO and who is working

on manifolds. And today he'll be talking about the rigging technique for one light light

soft manifolds. Please, you have the floor. Okay, thank you, Jemma, for the floor.

So, I want to share my, I want to share my screen. Okay, so just wait a moment.

Can you do it now? Is it possible? Okay, I see. Okay, I see the problem. Okay.

I want to, okay, now because of my problem, I put you as main host. Can you please give

permission to Hans to share his slides? Yes, Pao is the host. Yeah, I hope Pao is still there.

Pao, are you here? Are you there again? Yeah. Can you please give some administrative power

to Hans so that he can share his screen? Yeah. Okay, give me a second. Hans, where are you?

Hans, can you put Hans? Yeah, okay. Okay, now you can share your screen. Yes.

Okay, thank you. We are going to talk about rigging technique for one light light soft

manifold. I'm Hans Potsing from the University of Douala. I'm here in Erlangen since February

for a Russia visit with Professor Guring, at FAU,

and I thank him, I thank Guring for the opportunity. I would also like to thank the

FAU University as well as DFJ, which provided the funding. So I'm from the University of Douala

in Cameroon. Cameroon is a country in Central Africa sharing borders with Nigeria, Chad,

Congo, Equatorial Guinea, Gabon, and we have the Atlantic Ocean here, and Douala is somewhere here.

So the University of Douala is of course in Douala, more or less at the center of Douala,

and not far from Douala Airport. So if you plan to visit Douala, you can contact me to

visit the University of Douala as well. This is the main entrance of the first, the main campus

of the University of Douala. The building beyond there is the Amiseti building.

This is the campus of Lokbesu, where the Faculty of Science is now,

but lecturer's offices are not in this campus. My lecturer is not here.

My office is not here. So as you can see, the University of Douala is very clean, almost everywhere.

The University campus, sorry, I was not supposed to show this. That is a mistake. Okay.

So I'm from the western part of Cameroon, and more specifically I'm from Bamendju,

and this is my king since February, since 1953. He is 86 years old now.

Outline for this presentation.

So introduction.

So what I'm going to talk about is very different to what Pao just was talking about before.

So this is, I'm talking about a manifold and is somehow very pure mathematical subject.

And as introduction, to study the geometric geometry of every Semirimanjani ARP surface,

what people do most often is to project on the ARP surface orthogonally geometrical object of the ambient manifold.

And by so doing a new object on the ARP surface, we shall use to study the extrinsic geometry of the ARP surface.

But for lag light ARP surfaces are more general for one lag light so manifold,

the orthogonal projection is not possible. This is just because for lag light ARP surfaces,

every orthogonal vector is also tangent to the ARP surface.

So every orthogonal vector is also tangent to the ARP surface and then the orthogonal projection is not possible.

And we need new method to study the extrinsic geometry of a sub manifold embedded in a Semirimanjani manifold.

So people have proposed many methods and they turn out to be equivalent.

And then the first one I will talk about is based on string distribution.

So a string for a lag light ARP surface is a complementary of the orthogonal distribution

in the tangent distribution. As I said, the orthogonal

space is included in the tangent space.

So maybe I stop you a moment. So it seems like we have some delay. We cannot.

Now we can just see some three point of the slide. I don't know if we are going at the same pace as you are.

You cannot see my slide at the same time.

Yeah, so yeah, you cannot see them at the same time. So.

I don't know.