KNOWLEDGE AND UNDERSTANDING: becoming familiar with the
foundational results of Riemannian and Kaehler geometry.
APPLYING KNOWLEDGE AND UNDERSTANDING: developing the ability to
solve independently exercises in Riemannian and Kaehler geometry as
well as that of drawing simple corollaries from theoretical results proved
MAKING JUDGEMENTS: recognising and applying the basic techniques of
Riemannian and Kaehler geometry to relevant problems and situations.
COMMUNICATION SKILLS: achieving proficiency in the language of
Riemannian and Kaehler geometry.
LEARNING SKILLS: developing the ability to use with profit the main
textbooks in Riemannian and Kaehler geometry
Basic notions in differential topology and tensor calculus.
Riemannian metrics. Curvature. Hermitian
and Kaehler metrics. Elliptic theory on Riemannian manifolds. Hodge theory on Riemannian and Kaehler manifolds.
Traditional lectures will be complemented by example classes focussing
on the application of theoretical results. The active participation of
students will always be encouraged.
Oral exam. Initially candidates will be required to show their
understanding of the context, structure and proof of one or more of the
main theoretical results proved in lectures. Subsequently they will be
tested with respect to their ability to solve simple problems and to
produce relevant examples or counterexamples. The final mark will
reflect the outcome of these two steps.
Partial list of references
M. P. do Carmo, Riemannian Geometry, Birkhauser, 1992
J. Jost, Riemannian Geometry and Geometric Analysis, Springer-Verlag,
G. Tian, Canonical metrics in Kaehler Geometry, Birkauser 2000
D. Huybrechts, Complex Geometry, Springer-Verlang