Congruence of minimal surfaces and higher fundamental forms

 We show that minimal surfaces in space forms are determined, up to ambient isometries, by the induced metric and certain invariants which are defined in terms of the higher fundamental forms and the complex structure. Received: 6 May 2002 / Revised version: 5 July 2002 Current address: Institut für Mathematik, Universit?t Augsburg, Universit?tsstrasse 12, D-86135 Augsburg, Germany. e-mail: Theodoros.Vlachos@Math.Uni-Augsburg.De The author was supported by the Alexander von Humboldt Foundation Mathematics Subject Classification (2000): 53A10, 53C42 Acknowledgements. This work was written during the author's stay at the University of Augsburg as a research fellow of the Alexander von Humboldt Foundation. I wish to express my gratitude to the Alexander von Humboldt Foundation for its generous support. Moreover, I wish to thank Professor J.H. Eschenburg for many fruitful and stimulating conversations.