By Akira Fujiki (auth.), Junjiro Noguchi, Takeo Ohsawa (eds.)

In the Teichmüller thought of Riemann surfaces, along with the classical concept of quasi-conformal mappings, vari- ous techniques from differential geometry and algebraic geometry have merged lately. therefore the principal topic of "Complex constitution" used to be a well timed selection for the joint conferences in Katata and Kyoto in 1989. The invited members exchanged rules on varied techniques to comparable themes in advanced geometry and mapped out the clients for the following couple of years of research.

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**Additional resources for Prospects in Complex Geometry: Proceedings of the 25th Taniguchi International Symposium held in Katata, and the Conference held in Kyoto, July 31–August 9, 1989**

**Example text**

6. INTERVALS The purpose of this last section is to obtain a criterion for the existence of transversals to a set of intervals in Rn. By an interval we mean any connected subset of a line, so that they may also be open, rays or complete lines. A line being transversal to a set of intervals means that it does intersect all of them. 1 to intervals, requires the Hadwiger hypothesis of partial transversals compatible with a given linear order. Because 14 AROCHA, BRACHO AND MONTEJANO we have been working in projective space, where the general problem really lies, one other natural Hadwiger-type hypothesis to consider is compatibility with a given cyclic order.

O l r _ f c ; o n _ f c + i , o n _ f c + 2 , . . ,o n }, ij G { 1 , 2 , . . ,r — k belongs exactly to two classes containing the chosen ktuple ffki an(l therefore these (r — fc)-tuple belongs to exactly one such pair of classes. So, it must be true that (2) > ("l£)- Hence, zAi/-2(™~£) > 0. From this we get the desired inequality. : On a certain class of incidence structures. Prace a stiidie Vysokej skoly dopravnej v Ziline 2 (1979), 97-106. : On a connection between unit circles and horocycles determined by n points.

Geometry (ED. -R. Sack and J. Urrutia), pp. 633-701. V. North-Holland, Amsterdam, 2000. [5] C. H. Papadimitriou, and M. Yannakakis, Shortest paths without a map, Jour. Proc. 16th Internat. Colloq. on Automata, Languages, and Programming, Lecture Notes in Computer Science 372, 610-620, SpringerVerlag (1989). edu ''Donald R. edu ''Andras Bezdek'' A SHORT SURVEY OF (r,g)-STRUCTURES VOJTECH BALINT1 Department of Mathematics, University of Zilina, 010 26 Zilina, Slovakia. ABSTRACT. This contribution gives a short survey of results on the combinatorial (r, g)-structures as the generalization of many geometrical structures.