On the total absolute curvature of manifolds immersed in Riemannian manifolds. III (original) (raw)

The paper investigates the total absolute curvature of manifolds immersed in arbitrary Riemannian manifolds, extending previous work by Chern, Lashof, Kuiper, and Otsuki. It particularly focuses on surfaces within real space forms, examining specific cases regarding curvature conditions and their implications for the immersions. The findings highlight conditions under which the immersed manifolds exhibit particular geometric properties, offering insights into the relationship between immersion and curvature.