4 papers · 1 filter
A characterization of complex projective space via the Calabi curvature operator
Hasan M. El-Hasan, Xiaolong Li, Jan Nienhaus +3
We prove a Tachibana-type result for Kähler-Einstein manifolds isolating complex projective space based on its Calabi curvature operator. The proof uses a new Bochner formula expre…
Poincaré Polynomials and Curvature Operators of Symmetric Spaces
Peter Petersen, James Stanfield
We compute explicit formulas for the curvature operators and Poincaré polynomials of all compact irreducible symmetric spaces. We can easily derive the Poincaré polynomials using q…
Vanishing theorems for Hodge numbers and the Calabi curvature operator
Kyle Broder, Jan Nienhaus, Peter Petersen +2
It is shown that a compact -dimensional Kähler manifold with -positive Calabi curvature operator has the rational cohomology of complex projective space. For even $…
A general Schwarz lemma for Hermitian manifolds
Kyle Broder, James Stanfield
The Schwarz lemma for holomorphic maps between Hermitian manifolds is improved. New curvature constraints on the source and target manifolds are introduced and shown to be weaker t…