Curvature Operators on K\'{a}hler Manifolds

Autor:	Minemyer, Barry
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematical Physics Mathematics - Metric Geometry Primary 53C24 53C35 53C55 Secondary 53C15 53C20 53C21
Druh dokumentu:	Working Paper
Popis:	We prove that there exist K\"{a}hler manifolds that are not homotopy equivalent to a quotient of complex hyperbolic space but which admit a Riemannian metric with nonpositive curvature operator. This shows that K\"{a}hler manifolds do not satisfy the same type of rigidity with respect to the curvature operator as quaternionic hyperbolic and Cayley hyperbolic manifolds and are thus more similar to real hyperbolic manifolds in this setting. Along the way we also calculate explicit values for the eigenvalues of the curvature operator with respect to the standard complex hyperbolic metric.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.17101 Zobrazit plný text záznamu View this record from Arxiv