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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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Assoc. Prof. Ufuk Öztürk
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Instructors
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Assistants
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Resources
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K1. Lecture notes
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Supplementary Book
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YK1. Hacısalihoğlu, H.H. (2000). Diferensiyel geometri Cilt 2 (3. Baskı). Ankara Üniversitesi Fen Fakültesi, 340 s., Ankara.
YK2. Hacısalihoğlu, H.H. (2003). Diferensiyel geometri Cilt 3 (4. Baskı). Ankara Üniversitesi Fen Fakültesi, 206 s., Ankara.
YK3. Peterson, P. (2016). Riemannian geometry. (3rd ed.). Springer, 512 p., USA.
YK4. Aminov, Y. (2001). The geometry of submanifolds. CRC Press, 371 p., Singapore.
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Goals
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To introduce the fundamental concepts about Riemannian manifolds and to do operations on hypersurfaces.
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Content
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Riemannian manifold and covariant derivative; Hypersurfaces; Geodesics on hypersurfaces; Shape operator and Gauss map; Algebraic invariants of shape operator; Gauss equation and Gaussian curvature; Examples of hypersurfaces; Rotational hypersurfaces; Ruled surfaces; Invariants of ruled surfaces; Curves on Riemannian manifolds; Riemannian submanifolds; Generic Connections; Cartan equations
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Program Learning Outcomes |
Level of Contribution |
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1
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Improve and deepen the gained knowledge in Mathematics in the speciality level
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4
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2
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Use gained speciality level theoretical and applied knowledge in mathematics
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3
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Perform interdisciplinary studies by relating the gained knowledge in Mathematics with other fields.
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4
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4
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Analyze mathematical problems by using the gained research methods
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5
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Conduct independently a study requiring speciliaty in Mathematics
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5
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6
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Develop different approaches and produce solutions by taking responsibility to problems encountered in applications
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7
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Evaluate the gained speciality level knowledge and skills with a critical approach and guide the process of learning
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3
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8
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Transfer recent and own research related to mathematics to the expert and non-expert shareholders written, verbally and visually
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9
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Communicate with colleagues written and verbally by mastering a foreign language at least European Language Portfolio B2 General Level
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10
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Make use of the necessary computer softwares and information technologies related to Mathematics
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11
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Have the awareness of acting compatible with social, scientific, cultural and ethical values during the process of collecting, interpreting, applying and informing data related to Mathematics
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