Volume estimates for real hypersurfaces of a Kaehler manifold with strictly positive holomorphic sectional and antiholomorphic Ricci curvatures

Fernando Giménez and Vicente Miquel Molina

Vol. 142 (1990), No. 1, 23–39

DOI: 10.2140/pjm.1990.142.23

Abstract

We give some inequalities for the volume of a connected compact real hypersurface of a compact Kaehler manifold with strictly positive holomorphic sectional and antiholomorphic Ricci curvatures and prove that some of the corresponding equalities characterize the geodesic spheres in ℂPⁿ(λ).

Mathematical Subject Classification 2000

Primary: 53C55

Secondary: 53C40

Milestones

Received: 1 March 1988

Revised: 11 January 1989

Published: 1 March 1990