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Prerequisites
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Language of Instruction
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English
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Responsible
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Dr. Gül UĞUR KAYMANLI
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Instructors
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Assistants
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Resources
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R1. Ekici, C. (2021). Eğrilerin ve Yüzeylerin Geometrisi. Eskişehir Osmangazi Üniversitesi, Eskişehir.
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Supplementary Book
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SR1. Block, E. D. (1996). A First Course in Geometric Topology and Differential Geometry. Birkhauser, Boston.
SR2. O`Neil, B. (2006). Elementary differential geometry. Revised second edition. Elsevier/Academic Press, Amsterdam.
SR3. do Carmo, M. P. ( 2016). Differential geometry of curves & surfaces. Dover Publications, Mineola, NY.
SR4. Pressley, A. (2010). Elementary differential geometry. Second edition. Springer Undergraduate Mathematics Series, Springer, Berlin.
SR5. Hacısalihoğlu, H. H. (1998). Diferensiyel Geometri Cilt : 1 (3. Baskı). Hacısalihoğlu Yayınları, Anakara.
SR6. Sabuncuoğlu, A. (2010). Diferensiyel Geometri (4. Baskı). Nobel Akademik Yayıncılık, Ankara.
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Goals
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To teach basic notions and results of surfaces in classical differential geometry, and to provide necessary substructure to students who wish to study for a master degree in this area.
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Content
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Geometries and same related notions, affine space and Euclidean space; Topological manifold, diffeomorphism, differentiable manifold; Tangent vectors, tangent spaces and vector fields; Directional derivative, covariant derivative; Integral curve; Lie operator; Gradient divergence rotational function and the differential of a transformation; Curves and change of parameter; Serret-Frenet vectors; The osculating planes of a curve, curvatures and its geometric meanings; Curvature centers, osculating spheres; Some frame fields; Parallel curve pairs and involute evolute curve pair; Bertrand curve pair and Mannheim curve pair.
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