Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The
second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.
Kobayashi′s research spans the areas of differential geometry of real and complex variables, and his numerous resulting publications include several book:Foundations of Differential Geometry with
K. Nomizu,Hyperbolic Complex Manifolds and Holomorphic Mappings andDifferential Geometry of Complex Vector Bundles.