## "Babes-Bolyai" University of Cluj-Napoca Faculty of Mathematics and Computer Science

 Curves and surfaces
 Code Semes-ter Hours: C+S+L Credits Type Section MG001 2 2+1+0 5 compulsory Matematică MG001 2 2+1+0 5 compulsory Informatică MG001 2 2+1+0 4 compulsory Matematică-Informatică MG001 2 2+1+0 5 compulsory Matematici Aplicate
 Teaching Staff in Charge
 Assoc.Prof. VARGA Csaba Gyorgy, Ph.D., csvarga@cs.ubbcluj.roAssoc.Prof. PINTEA Cornel, Ph.D., cpintea@math.ubbcluj.roLect. VACARETU Daniel, vacaretu@math.ubbcluj.roLect. BLAGA Paul Aurel, Ph.D., pablaga@cs.ubbcluj.ro
 Aims The course gives to the students the principal tools and also the necesary methods in the study of curves and surfaces with an accent on the intuitive side.
 Content I. Local theory of curves. 1. Curves in euclidean space.Tangent line and normal plane. 2. Curves in general position. Osculating plane. 3. Frenet frame. Frenet formulas. Curvature and torsion. 4. Geometric iterpretation of curvature and torsion. 5. Contact beatween two curves. 6. Evolute and involute. 7. Envelope of a family of curves in plane. II.Local theory of surfaces. 1. Surfaces in three-dimensional euclidean space. 2. Tangent plane and normal line of a surface. 3. First fundamental form of a surface. 4. Arc length , angle between two curves on surface .Area element. 5. Second fundamental form. 6. Normal curvature. 7. Asymptotic lines of a surface. 8. Principal curvatutres of a surface. Mean curvature and Gaussian curvature. 9. Theorema egregium. 10.Minimal surfaces and surfaces with constant curvature. 11.Darboux frame. Darboux formulas. 12.Geodesic curvature. Geodesic torsion. 13.Geodesic lines.
 References 1. L. Nicolescu, Curs de geometrie, Bucuresti 1990 2. A. Dobrescu, Geometrie diferentiala, Ed. Did. si Ped. Bucuresti 3. doCarmo, M.P. Differential Geometry of Curves and Surfaces, Eglewood Cliffs, N.J. Pretince-Hall, 1976 4. C. Pintea, Geometrie, Presa Universitara Clujeana, 2001. 5. F. Rado, G. Galbura, Geometrie, Ed. Did. si Ped., Bucuresti, 1978. 6. Enghis, P., Tarina, M., Curs de geometrie diferentiala (lito) Univ. Cluj-Napoca, 1987.
 Assessment Exam.