Date

1966

Document Type

Thesis

Degree

Master of Science

Department

Mathematics

First Adviser

Hsiung, Chuan Chich

Abstract

In the last three decades, differential geometry has been developed in the direction of studying the relationships between the local differential properties of a manifold and its topological structure as a whole. Along this direction the first important result was contributed by W. V. D. Hodge in 1936. S. Bochner in 1946 and A. Lichnerowicz in 1948 applied Hodge's theorem to obtain curvature conditions for a compact orientable Riemannian manifold to have vanishing homology. In 1951 H. E. Rauch introduced interesting pinched Riemannian manifold, and in 1960 M. Berger continued Rauch's work to study the homology of those manifolds. The purpose of this thesis is to study these results in details.

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