16-22 September 2019
Title of the course: Spinc structures on manifolds and geometric applications
Instructor: Assoc. Prof. Roger Nakad
Institution: Notre Dame University Lebanon
Dates: 16-22 September 2019
Prerequisites: Linear Algebra, Riemannian Geometry
Level: Graduate
Abstract: These lecture series aim to give an elementary exposition on basic results about the first eigenvalue of the Dirac operator, on compact Riemannian Spin and Spin^c manifolds and their hypersurfaces. For this, we select some key ingredients which illustrate the basic objects and some of their properties as Clifford algebras, spin and spin^c groups, connections, covariant derivatives, Dirac and Twistor operators. We end by giving beautiful geometric applications: a Lawson type correspondence for constant mean curvature surfaces in some 3-dimensional Thurston geometries, extrinsic hyperspheres in manifolds with special holonomy, Alexandrov type theorems…
Language: EN
Instructor: Assoc. Prof. Roger Nakad
Institution: Notre Dame University Lebanon
Dates: 16-22 September 2019
Prerequisites: Linear Algebra, Riemannian Geometry
Level: Graduate
Abstract: These lecture series aim to give an elementary exposition on basic results about the first eigenvalue of the Dirac operator, on compact Riemannian Spin and Spin^c manifolds and their hypersurfaces. For this, we select some key ingredients which illustrate the basic objects and some of their properties as Clifford algebras, spin and spin^c groups, connections, covariant derivatives, Dirac and Twistor operators. We end by giving beautiful geometric applications: a Lawson type correspondence for constant mean curvature surfaces in some 3-dimensional Thurston geometries, extrinsic hyperspheres in manifolds with special holonomy, Alexandrov type theorems…
Language: EN