6533b831fe1ef96bd1298d25
RESEARCH PRODUCT
Comparison theorems for the volume of a complex submanifold of a Kaehler manifold
Fernando GiménezFernando Giménezsubject
Pure mathematicsHypersurfaceGeneral MathematicsMathematical analysisHolomorphic functionComplex dimensionKähler manifoldAlgebra over a fieldSubmanifoldQuotientMathematicsVolume (compression)description
LetM be a Kaehler manifold of real dimension 2n with holomorphic sectional curvatureK H≥4λ and antiholomorphic Ricci curvatureρ A≥(2n−2)λ, andP is a complex hypersurface. We give a bound for the quotient (volume ofP)/(volume ofM) and prove that this bound is attained if and only ifP=C P n−1(λ) andM=C P n(λ). Moreover, we give some results on the volume of of tubes aboutP inM.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1990-12-01 | Israel Journal of Mathematics |