S. IANUS and G. B. RIZZA
On totally umbilical holomorphic submanifolds
Pages 15-23
Received: 18 June 1999
Mathematics Subject Classification (2000): 53B25 - 53C40
Abstract Let M be a holomorphic totally umbilical submanifold of an almost Hermitian manifold \tilde{M}. Some relations for biholomorphic and mixed curvatures of M and the corresponding curvatures of \tilde{M} are obtained. When these curvatures are assumed to be constant on \tilde{M}, we derive lower and upper bounds for the corresponding curvatures of M. Similar results are true for some known expressions involving sectional and bisectional curvature. Hereditary properties for AH2-manifolds, for AH3 -manifolds, for almost constant type manifolds and for constant type manifolds are also derived.