HARMONIC AND TOTALLY GEODESIC MAPPINGS

【摘要】 <正> Suppose that f:M→M′ is a C^∞ mapping of Riemannian manifolds and g’ is the metric tensor of M’, If f^*g’, the first fundamental form of f, is the parallel section in the bundle ²T^*M, then we call f the relatively affine mapping. Taking df, the differential of f, as f^-1TM’-valued 1-form, we define B（f）, the second fundamental form of f, as the covariant differentiation df. The mapping更多还原