1. He did not grant independent existence to the non-euclidean geometries . 2. In the case of non-euclidean geometry he published no definitive work . 3. The advent of the theory of relativity forced a drastic change in the attitude toward non-euclidean geometry . 4. It was this concept that riemann generalized, thereby opening up new vistas in non-euclidean geometry . 5. But none of the mathematicians believed that these basic non-euclidean geometries would be physically significant . 6. Gaussian intrinsic differential geometry and non - euclidean geometry 7. This cumulative development of mathematics applies especially to non - euclidean geometry 8. It was this concept that riemann generalized , thereby opening up new vistas in non - euclidean geometry 9. Another reason for the loss of interest in the non - euclidean geometries was their seeming lack of relevance to the physical world 10. Aim to study the relations between the thought of gaussian intrinsic differential geometry and gauss ' s earlier research on non - euclidean geometry
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