CANKIRI KARATEKIN UNIVERSITY Bologna Information System


  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Minimal Submanifolds MAT534 FALL-SPRING 3+0 E 6
    Learning Outcomes
    1-To comprehend minimal submanifolds
    2-To give Weierstrass type representations
    3-To comprehend stable minimal hypersurfaces
    4-To comprehend entire spacelike submanifolds
  • ECTS / WORKLOAD
  • ActivityPercentage

    (100)

    NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14342
    Classroom study (Pre-study, practice)14570
    Assignments2041040
    Short-Term Exams (exam + preparation) 0000
    Midterm exams (exam + preparation)3011414
    Project0000
    Laboratory 0000
    Final exam (exam + preparation) 5011818
    Other 0000
    Total Workload (hours)   184
    Total Workload (hours) / 30 (s)     6,13 ---- (6)
    ECTS Credit   6
  • Course Content
  • Week Topics Study Metarials
    1 The first variational formula
    2 Rigidity theorems
    3 Bernstein`s theorem and its generalizations
    4 The Weierstrass representation
    5 The representation for surfaces of prescribed mean curvature
    6 The representation for CMC-1 surfaces in H3
    7 Hyperbolic Gauss maps
    8 Stable minimal hypersurfaces
    9 Curvature estimates for minimal hypersurfaces
    10 Harmonic Gauss maps
    11 Bernstein type theorems
    12 A Bochner type formula
    13 Estimates of the second fundamental form
    14 Bernstein problem
    Prerequisites -
    Language of Instruction Turkish
    Responsible Assist. Prof. Dr. Ufuk ÖZTÜRK
    Instructors -
    Assistants The related lecturers of the department
    Resources 1) Y. Xin, 2003. Minimal submanifolds and related topics. World Scientific, 262 p., Singapore. 2) H. Anciaux, 2011. Minimal submanifolds in pseudo-Riemannian geometry. World Scientific, 167 p., Singapore.
    Supplementary Book -
    Goals -
    Content To define minimal submanifolds and to solve Bernstein type teorems.
  • Program Learning Outcomes
  • Program Learning Outcomes Level of Contribution
    1 Improve and deepen the gained knowledge in Mathematics in the speciality level 5
    2 Use gained speciality level theoretical and applied knowledge in mathematics 5
    3 Perform interdisciplinary studies by relating the gained knowledge in Mathematics with other fields. 2
    4 Analyze mathematical problems by using the gained research methods 4
    5 Conduct independently a study requiring speciliaty in Mathematics 5
    6 Develop different approaches and produce solutions by taking responsibility to problems encountered in applications 5
    7 Evaluate the gained speciality level knowledge and skills with a critical approach and guide the process of learning 3
    8 Transfer recent and own research related to mathematics to the expert and non-expert shareholders written, verbally and visually 5
    9 Make use of the necessary computer softwares and information technologies related to Mathematics -
    10 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 4
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