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Geometry and topology of Riemannian varieties

Abstract

The general objective of this project is the study of the topology of the Riemannian varieties with extrinsic and intrinsic metric restrictions. The principal topics are: a) sub-varieties of the IRn with non-negative curvature operator or with second fundamental form parallel; b) construction of metrics with non-negative curvature in fibered varieties; c) relationship of the items above with variational methods, including the energy functions, of Yang-Mills, of area and volume, with or without link, which includes harmonic applications; d) generalized theory of Morse and the study of orbits of Lie groups in the context above. (AU)

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