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Course Information

Course Information

Course Title	Code	Semester	L+U Hour	Credits	ECTS
SEMI-RIEMANN GEOMETRY II	801500805360		3 + 0	3.0	10.0

Prerequisites

None

Language of Instruction	Turkish
Course Level	Graduate Degree
Course Type	Compulsory
Mode of delivery	Face to face
Course Coordinator
Instructors
Assistants
Goals	The tangent space of a manifold in a two-dimensional manifold would be. Their tangent and cotangent bundles of a manifold is to introduce.
Course Content	Semi-Riemannian manifolds. Tangent and normal spaces. Reduced connection. Geodesic curves in the submanifolds. Total geodesic manifolds. Semi-Riemannian hypersurfaces. Hiperkuadriks. Codazzi equation. Totally umbilical hypersurfaces. Other connection. Isometric immersions. Transformations with two-parameter. Gauss's lemma. Convex open sets. Arc length. Riemann distance. Completeness in terms of Riemann. Lorentz causal character. Timecones. Local Lorentz geometry. Geodesics in hiperkuadrik. Geodesics in surfaces. Orientation. Semi-Riemannian covers. Lorentz time orientation. Volume element. Jakobi vector fields. Locally symmetric manifolds. Semi-orthogonal groups. Some isometry groups
Learning Outcomes	1) To introduce the tangent and cotangent bundles of a manifold 2) To get information about semi-Riemann manifolds 3) To get information about semi orthogonal group.