Given a mathematical structure, one of the basic associated
mathematical objects is its automorphism group. The object of this
book is to give a biased account of automorphism groups of
differential geometric struc tures. All geometric structures are
not created equal; some are creations of ods while others are
products of lesser human minds. Amongst the former, Riemannian and
complex structures stand out for their beauty and wealth. A major
portion of this book is therefore devoted to these two structures.
Chapter I describes a general theory of automorphisms of geometric
structures with emphasis on the question of when the automorphism
group can be given a Lie group structure. Basic theorems in this
regard are presented in 3, 4 and 5. The concept of G-structure or
that of pseudo-group structure enables us to treat most of the
interesting geo metric structures in a unified manner. In 8, we
sketch the relationship between the two concepts. Chapter I is so
arranged that the reader who is primarily interested in Riemannian,
complex, conformal and projective structures can skip 5, 6, 7 and
8. This chapter is partly based on lec tures I gave in Tokyo and
Berkeley in 1965."
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