Die Reduktion von nichteuklidischen geometrischen Objekten in eine euklidische Form und physikalische Deutung der Reduktion durch Eigenspannungszustände in Kristallen

Summary Self-stresses in crystals are closely related to tearing processes. These processes have a meaning only in connection with geometrical objects. The present paper deals with tearing processes connected with the geometrical objects metric and connexion. A tearing process is commonly associated with either one of these processes. It is therefore of interest to investigate the question whether a tearing process which is connected with both objects exists. The investigation of this problem leads to the subdivision of the self-stresses according to the metric properties of the connexion: metrical stresses caused by dislocations and disclinations and nonmetrical stresses caused by non-mechanical sources and by extra-matter.It should be mentioned that the mathematical part of this paper has an independent interest for the understanding of the structures associated with higher differential geometry.

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Vorgelegt von T. Meixner

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Herrn Professor Dr. A. Seeger danke ich für die verständnisvolle Förderung dieser Arbeit. Herrn Dr. C. Teodosiu bin ich für zahlreiche Diskussionen sehr dankbar.

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