Mathematical Sciences: Some Curvature Problems in Riemannian Geometry

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9404312 Yang The topics proposed in the research entail curvature estimates on classes of four-dimensional manifolds. This also includes a study of the geometry of actions of the integer modulo p-group where for p equal to a prime number it is intended to prove a homeomorphism classification theorem for nonnegative sectional curvature. Deformations of exotic differentiable structures on the 7-sphere will also be analyzed. The research has potential applications to topology and gauge field theory in mathematical physics. ***