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 Announcement of Seminar Cairo-2005
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The first international scientific workshop
“Geometry of Finsler spaces with the Berwald-Moore metric”
15 – 22 October 2005
Cairo, Egypt
Dear Colleagues!
Finsler geometry is a natural extension of Riemann geometry and keeps its true potential in itself. The formal description of Finsler geometry is quite complicated. Therefore, it is considered as an object of abstract mathematical investigations. Nevertheless, there are solid reasons to think that even the simplest spaces with non-quadratic types of metrics, which are very close to well-known Euclidian and pseudo-Euclidian spaces, directly relate to the fundamental problems of theoretical physics.
The main topic of discussions of the international workshop is the Finsler geometry with the Berwald – Moore’s metric. The choice of this metric function is due to the following reasons.
1. The Berwald – Moore’s metric is the simplest one of nondegenerated Finsler metrics.
2. It is isomorphic to the well-known metric of pseudo-Euclidian plane in the case of two-dimensional space.
3. The Berwald – Moore’s metric is in close connection with the fundamental mathematical concept – the real number, and provides the geometrical interpretation of several hypercomplex algebras (designated as Hn), based on the regular commutative and associative laws for addition and multiplication.
4. Nowadays the Berwald – Moore’s metric is one of the few known Finsler metric functions which is consistent with the observed signature of real space-time (+ – – – ).
The workshop is planed to be held in Cairo, Egypt, on 15-22 October 2005. The location of the workshop is chosen with regard to the tradition to visit Egypt in search of new knowledge. The season is the best for Egypt climate. More over, the abundance of historical places, famous ancient temples and great pyramids makes the free-time very interesting.
Works, devoted to the geometric research of Finsler spaces with the Berwald – Moore’s Finsler metric function and corresponding hypercomplex algebras Hn, will be included in the workshop program. In particular, the main directions of the workshop:
1. Generalized algebraic properties of the hypercomplex numbers Hn;
2. Main geometric objects of the spaces with Berwald-Moor metric and their differences from Euclidian analogues;
3. Metric invariants and corresponding transformations;
4. Analytical functions of hypercomplex numbers Hn;
5. Generalization of the concept of analyticity;
6. Conform transformations;
7. Generalization of conform transformations;
8. Problem of convergence for a sequence of points;
9. Fractal objects.
10. Physical interpretations of spaces with the Berwald – Moore’s metric;
11. The limit correspondence between the Berwald – Moore’s space and Minkowski and Galilei spaces.
12. The experimental search for the real space-time anisotropy characteristic to Finsler spaces.
The Organizing Committee plans to compensate a part of traveling and accommodation expenses.
Abstracts of reports and applications of participation (registration forms) should be sent by the e-mail hypercomplex@mail.ru
We plan to issue the abstracts before the workshop. The most interesting reports will be published in the journal “Hypercomplex numbers in geometry and physics” in Russian and English after the workshop.
References on the spaces with the Berwald-Moor metric
1. G. Yu. Bogoslovsky, H. F. Goenner: Phys. Lett. A 244, N 4, (1988) 222.
2. G. Yu. Bogoslovsky, H. F. Goenner: Gen. Relativ. Gravit. 31, N 10, (1999) 1565.
3. G. S. Asanov: Finslerian Extension of General Relativity, Dordrecht, 1984.
4. H. Rund: Differential Geometry of Finsler Spaces, addition by G. S. Asanov.
In Russian: Õ. Ðóíä. Äèôôåðåíöèàëüíàÿ ãåîìåòðèÿ ôèíñëåðîâûõ ïðîñòðàíñòâ. Ì., "Íàóêà", 1981., äîïîëíåíèå II, íàïèñàííîå Ã. Ñ. Àñàíîâûì. File see here )
5. “Hypercomplex numbers in geometry and physics” N 1, (2004), electronic version
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